It was Nemanja Matić who stole the show, however. The former Chelsea man, who moved to Old Trafford for £40million in the summer, was a colossus in the centre of midfield.
There were four debutants on show for West Ham, including former United star Javier Hernández. But none of the quartet made a significant impression as the Irons were dominated from start to finish.
We've rated the players' performances at Old Trafford. If you agree or disagree, tweet us at @FB_Whispers.
David De Gea
The Spaniard, who was once again the subject of Real Madrid transfer rumours this summer, had a comfortable and quiet first Premier League appearance of the season.
He made one first half save to deny Edimilson Fernandes and was rescued by the crossbar for a Marko Arnautović header. But it was otherwise an easy afternoon for De Gea. 6
The Ecuadorian was Manchester United's 2017 Player of the Season and he picked up from where he left off against the Hammers.
Valencia's transition from winger to full-back has been seamless and he is constantly improving the defensive side of his game.
He made two tackles against the Hammers and one interception. There are rumours United may sign Serge Aurier from PSG but if that deal goes ahead, it will be difficult for the Ivorian to oust Valencia. 7
In just over a year the Ivorian defender has gone from being somewhat of an unknown to Manchester United's first choice centre-back.
There are few floors in Bailly's armoury. He reads the game well, is quick across the ground and has the physical attributes needed to compete with even the most powerful of Premier League strikers.
He kept Hernandez and then Diafra Sahko quiet throughout the game, making just the one tackle and interception in the process. 7
When Jones is fit, he is a fine defender and he proved that against the Hammers.
The former Blackburn Rovers centre-back is surprisingly quick across the ground and reads the game well. He is also willing to dive into tackles, no matter where he is on the pitch.
Jones completed two tackles and made three interceptions. If he can avoid injury, then he could be the perfect partner for Bailly. 7
United's ultimate utility man started at left-back in the absence of Luke Shaw and was his usual reliable self.
Blind made one tackles, two interceptions and five clearances, the highest of any Manchester United player. He also came close with a second half volley that ended up bouncing onto the roof of the net. 7
If Chelsea manager Antonio Conte was watching the game, you imagine he'd have turned off the television at half time in anger. Matic was, quite simply, superb on his Premier League debut for Manchester United.
Many questioned the £40million fee the Red Devils paid but the Serbian has quickly rediscovered his best form after reuniting with Jose Mourinho at Old Trafford.
Matic dominated West Ham's midfielders, slalomed past opposition players and was instrumental in United's opener by closing down Pedro Obiang.
If he continues in this form, then Matic's signing may prove to be one of the best of the season. 9
There is little doubt Manchester United's record signing is most comfortable playing on the left of a midfield three. So where did he start against West Ham? On the right of a midfield two, naturally.
Pogba, however, is a supremely gifted footballer and his ability on the ball means that no matter where he's deployed, he can make a difference.
He played one delightful first half pass which created a chance for Mata and covered plenty of ground alongside Matic.
Mourinho has tasked Pogba with scoring more goals this season and he rounded United's win off with an excellent fourth late on. 7.5
The diminutive Spaniard was used as United's No.10 and was influential in the opening period.
Mata had two excellent chances to open the scoring. The first was saved by Joe Hart while he attempted to tee up Lukaku with the latter but didn't put enough on his pass.
He was brought off after 75 minutes as the game become stretched. 7
Now in his second season at Old Trafford, many a United fan will be hoping the Armenian finally produces his best football for the club.
Playing on the right of an attacking three, Mkhitaryan showed several neat touches to help the Red Devils keep possession and it was his free-kick that led to Lukaku's second.
His influence grew as the second half progressed and he was unfortunate not to get on the scoresheet. Mkhitaryan ended the game having played six key passes, by far the most of any United player 8
After the signing of Lukaku, it's likely that Rashford is going to have to get used to starting on the left flank for Manchester United. And while he is clearly not a natural in the role, he is improving.
He offers a threat when cutting inside and it was the 19-year-old who launched the counter attack from which United broke the deadlock in the 33rd minute.
West Ham defender Pablo Zabaleta struggled to contain Rashford in the second half and he was unlucky not to open his account for the season with a thunderous shot that rattled the post. 7.5
The hulking Belgian scored on his Premier League debut for West Bromwich Albion and for Everton, so there was a certain inevitability about his first appearance for Manchester United at Old Trafford.
After a quiet opening half an hour, Lukaku demonstrated why the Red Devils paid £75million to sign him by rounding off an excellent counter attack with a clinical finish.
He then headed home his second and only an excellent block from Zabaleta denied Lukaku a debut hat-trick. 8.5
Fellaini for Mata (75): Was brought on to shore up the midfield. A job the Belgian is perfect for. 6
Martial for Rashford (79): Had eleven minutes to make his mark and did just that, scoring United's third goal with a coolly taken finish. 7
Lingard for Mkhitaryan (87): N/A
West Ham United
Back in English football after a loan spell with Torino last season, Hart would've wanted to make a statement as to why he remains England's No.1.
He made an excellent first half save to deny Mata but could do nothing to stop either of Lukaku's goals.
Hart was beaten twice late on, too, and perhaps could've done better to deny Pogba's shot from distance. 6
The Argentine joined West Ham from Manchester City on a free transfer this summer and, while he may not be the force he once was, there is no denying his commitment to the cause.
Zabaleta was caught out of position for Lukaku's opening goal but made up for that with an excellent second half block to deny the Belgian from completing his hat-trick.
However, he struggled to contain Rashford for much of the game and was booked for bringing down the England international. 5
He is short of match fitness, however, but still made three interceptions, a team high. 5
The Italian made more clearances (seven) than any of his West Ham team-mates but he, like Reid, failed to keep Lukaku in check.
Ogbonna should've done more to track Martial for United's third but his performance wasn't the worst of West Ham's back four. 5
The French defender was selected ahead of Aaron Cresswell because of the English left-back's hamstring complaint, but his performance is unlikely to see him remain in the starting XI.
Masuaku never looks entirely comfortable on the ball and was at fault for United's second goal.
In the build-up to a free kick, he was seen laughing with Lukaku before attempting to readjust his shin pads moments before the ball was put into the box.
He then failed to track Lukaku's run and the Belgian headed home. Masuaku's final involvement in the game was to let a simple pass roll underneath his foot and out of play. It summed up his afternoon. 4
The West Ham captain worked hard in the first half to restrict space and stifle the influence of Mata.
He also teed up the Hammers' best chance of the game with a clever flick moments before half time. However, Noble faded after the break and was brought off on the hour.
He did make four interceptions and played three key passes during his time on the pitch and was West Ham's best midfielder on the day. 6
No West Ham player attempted more passes than Obiang's 55 but one that was intercepted proved the most costly.
The midfielder tried to pick out a run from Zabaleta in the first half but Matic was quickly into block the pass. The ball fell to Rashford who would go on to set-up Lukaku for United's opener.
Obiang was nervy in possession thereafter and gave the ball away more than once in the second period. 5
A very ineffective performance from the midfielder. He failed to make a single tackle or interception and only played 19 passes before being brought off in the 59th minute.
Fernandes did, however, have West Ham's best chance of the game with a shot which was straight at de Gea. 5
He covered plenty of ground but Ayew isn't a winger and that was evident at Old Trafford.
He was on the periphery of the contest throughout the 90 minutes and failed to register a shot on goal or play a pass of significance. 5
West Ham spent £22million to sign Arnautović from Stoke City and he did come closest to scoring for the visitors with a header that clipped the crossbar.
But the Austrian will be expected to offer more than he showed at Old Trafford throughout the rest of the season. His set-pieces were also poor. 5
The Little Pea returned to the stadium he called home for five years looking to make an impact for new club West Ham.
But, unfortunately for the Mexican, he saw very little of the ball and never looked like threatening his old side.
The closest Hernandez came was with a late shot that drifted over the crossbar. But he worked hard throughout the contest, which is more than could be said for some of his team-mates. 6
Sahko for Fernandes (59): Had 30 minutes to make an impact yet did nothing. 5
Rice for Noble (59): Brought some urgency to the West Ham midfield but couldn't influence the game 6
Cresswell for Masuaku (81): N/A