Craig Shakespeare's side had turned the game around to lead 3-2 going into the final ten minutes of the contest but Aaron Ramsey equalised for the Gunners before Olivier Giroud headed home a winner in the 85th minute.
The victory is only Arsenal's second opening weekend success in the last seven years. They will not have to chase the leading pack come Monday, which looked a distinct possibility for much of the evening.
But it was far from a flawless performance from Arsenal. Their defenders, in particular, struggled with Jamie Vardy, who was at his best for the Foxes. New signing Harry Maguire impressed, too.
And we've rated the players' performances at the Emirates. If you agree or disagree, tweet us at @FB_Whispers
This season will be the Czech's 14th in the Premier League but it didn't get off to the best of starts as he was caught out of position in the build-up to Shinji Okazaki's equaliser.
Cech could do little about either of Vardy's two goals, however, and was quickly off his line in the second period to deny the England striker from breaking through on goal.
The Arsenal No.1 was also a calm influence late on, collecting loose balls in the penalty area twice in succession. 6
The 21-year-old impressed after coming into the Arsenal defence at the back end of last season but he always had an experienced central defender alongside him.
Without the influence of Laurent Koscielny or Shkodran Mustafi in the Gunners' back three, Holding was shaky throughout against Leicester.
He was caught on the ball more than once while trying to play out of defence and struggled with the pace of Vardy. It will be an experience Holding can learn from but a night he'd probably rather forget. 5.5
The 31-year-old is a fine left-back and a more than competent wing-back. What he isn't, however, is a centre-back and Vardy ruthlessly exposed that on more than one occasion.
Monreal struggled to keep the England striker in check throughout the game and he didn't track Vardy's run for Leicester's second goal. He was also out-jumped by the Leicester No.9, who glanced a header into the far corner.
The Spaniard is unlikely to play in the heart of the Arsenal defence too often, and on the basis of this display that isn't a bad thing for the Gunners. 5.5
The Bosnian is likely to be good fun to watch this season, for the right and wrong reasons. His first major involvement in a Premier League game was to wander off from his back post position and allow Maguire the room to tee up Okazaki.
However, going forward Kolašinac is a powerhouse and a threat. He forced Kasper Schmeichel into a smart stop in the first half and broke forward to set up Danny Welbeck's close range finish.
He also demonstrated his ability to win the ball back. Kolašinac completed four successful tackles, the joint highest of any Arsenal player. 6.5
Deployed at right wing-back, the Spaniard had a understated but effective night. He played two key passes and won three tackles but he didn't have a huge impact on the match.
Bellerin also didn't give Holding a great deal of support as Leicester, through Marc Albrighton, launched several attacks down the Arsenal right.
But the Spain Under-21 international is still regaining his confidence after a difficult 2016/17 campaign, so he should improve as the season progresses. 6
The Swiss midfielder looked to have turned a corner after excellent performances in the FA Cup final and Community Shield, but he was patchy against the Foxes.
Xhaka gave the ball away cheaply in the build-up to Leicester's second goal and didn't impose himself in midfield. His distribution was also inconsistent as only 81.8 per cent of passes found a team-mate.
Crucially for Arsenal, though, one that did led to Ramsey equalising for the home side. There is more to come from Xhaka but he can't afford to let the game pass him by for long stretches. 6.5
When Arsenal have a fully fit squad, Elneny doesn't play. It's that simple. He is a squad player who lacks the quality to start every week for a top four club, and that showed against Leicester.
While the Egyptian worked hard and closed down the Foxes midfielders – he made four tackles and one clearance – with the ball he was largely ineffective.
Yes, he teed up the opening goal with a clipped cross but he offered little else. It was little surprise that he was sacrificed as Arsenal search for a route back into the game. 6
A mixed evening for the England international. He was started at left wing-back but was shunted over to the right flank in the second half. Neither are his preferred position but he got on with the job in hand.
But Oxlade-Chamberlain lacked composure as Arsenal searched for a way back into the game, taking several shots that failed to hit the target. He only worked Schmeichel twice from six attempts. 6
Few players work as hard as Welbeck but whether he has the quality to nail down a starting berth in the Arsenal side remains to the seen.
He saw a first half effort blocked before levelling on the stroke of half time, although he nearly wasted the chance as he struggled to sort out his feet.
Welbeck is a willing worker, though, and will follow the instructions given to him to the letter. That means there will also be a place for him at Arsenal, it just may not always be in the starting XI. 7
The German wasn't fully fit but was instrumental in the Gunners' victory. So much of what Özil does can be missed but he is the orchestrator of the Arsenal attack.
He played six key passes and completed two dribbles, while also completing 86.4 per cent of his passes. No Arsenal attacker had as much influence over the course of the 90 minutes. 7
The French striker needed less than two minutes to make his mark in the Premier League.
His goal was excellently taken and was the mark of a natural finisher. His celebration was one of a man confident in his ability.
Lacazette linked play throughout – he played three key passes – and only an excellent save from Schmeichel denied him a second goal on his debut. 7.5
Giroud for Holding (66): The French striker may not want the tag but he is becoming a super sub. He offered Arsenal something different after his introduction and took his goal superbly. 8.5
Ramsey for Elneny (66): Much more of a threat than the man he replaced. The Welshman displayed excellent composure to equalise with seven minutes to play. 8.5
Walcott for Welbeck (74): Thrown on with Arsenal behind, the Gunners turned the game around with Walcott on the field. But their comeback wasn't down to the winger. 6.5
The Foxes' No.1 goalkeeper could do little do stop any of the four Arsenal goals and, if it wasn't for his quick reactions to deny Lacazette with a stunning stop, the Gunners would've levelled much earlier than the 83rd minute.
Schmeichel also played the most passes, 33, of any Leicester player – a mark of the Gunners' dominance with the ball. 7
Not the most glamorous of full-backs in the Premier League but Simpson is consistent and was effective against Arsenal.
He restricted the threat of Oxlade-Chamberlain in the first half and made one important interception as Arsenal pushed for an equaliser. 6.5
The 33-year-old let Lacazette slip away from him for Arsenal's opening goal but he improved throughout the game and made several important blocks to keep the Gunners, temporarily, at bay.
Morgan made four clearances and one interception but couldn't stop Arsenal from completing a late turnaround. 6.5
Leicester paid £17million to bring in Maguire from Hull City and on the basis of his performances at the Emirates, it may go down to be one of the signings of the season.
The 24-year-old was everything Arsenal's defenders weren't; assured, brave and determined. He was also comfortable in possession and helped start many a Leicester attack.
However, it was the defensive side of his game that really stood out. Maguire made one crucial block to deny Welbeck in the first half and also made two crucial interceptions to end Arsenal attacks.
He did, however, get bullied by Giroud for Arsenal's winner which spoiled an otherwise faultless display. 7.5
The left-back kept Bellerin quiet for most of the evening but rarely ventured beyond his own half way line.
Fuchs is a reliable defender and he has an excellent long throw in his armoury, however, with Ben Chilwell's continued improvement, the Austrian may find it difficult to keep his place in the side throughout the season. 6.5
Given the Algerian admitted he wanted to leave Leicester this summer, with Arsenal said to be interested, it is a surprise he remains with the Foxes.
And despite speculation about his future, Shakespeare had no qualms naming Mahrez in his side at the Emirates. It was a gamble. Would he perform in front of the cameras or would he go into his shell?
The winger certainly didn't let Leicester down. He was a constant threat and it was from his excellent corner that Vardy scored the Foxes' third. It may have just been a display to highlight his quality to potential suitors but it was one that was important for Leicester. 7
A quiet night from the young midfielder who was linked with a move to Manchester United during the summer.
Ndidi was far more reserved than during the second half of last season and didn't have a huge effect on the game – he completed a dismal 61 per cent of his passes attempted. 6
James' start at the Emirates was his first in the Premier League in 832 days. That is partly down to falling out of favour but largely because of a knee injury he sustained in May 2015.
It's been a long road back for James but, after impressing in pre-season and an injury to Danny Drinkwater, the 26-year-old was given a chance in the starting XI.
He didn't let Shakespeare down. James covered plenty of ground, made four tackles, the highest of any Leicester player, and two interceptions.
He may have been more limited with the ball but it was no coincidence Leicester crumbled after he left the field. 7
There is nothing particularly fancy about Albrighton. He is an old-fashioned winger who when he gets the ball, looks to put in a telling cross. And two of his deliveries resulted in Leicester goals.
The first was headed back across goal by Maguire and nodded in by Okazaki while the second was put on a plate for Vardy who tapped into an empty net from close range. 7
The Japanese international was his usual busy self and he got into the right position to nod home Maguire's knock back early into the game.
He didn't offer a great deal else, however, and it was little surprise he was replaced with just under 20 minutes to play.
There is little doubt Okazaki's place is under threat and Kelechi Iheanacho, once fit, may force him out of the starting XI. 6.5
It was a little over a year ago that the England striker turned down a move to the Emirates and Vardy played like a man with a point to prove.
Arsenal's back three couldn't deal with the Leicester No.9's movement and pace. They were constantly on edge and that nervousness spread around the team.
Vardy was also clinical. He expertly found space for his first and did brilliantly to out-jump Monreal and glance the ball home for his second. He was the stand-out performer on the night. 9
Amartey for Okazaki (71): Offered little protection following his introduction. 6
Iheanacho for James (81): N/A
Gray for Albrighton (88): N/A