After a goalless opening 45 minutes, Granit Xhaka's deflected shot shortly after the restart put the Gunners ahead. Former United star Danny Welbeck then doubled the hosts' lead with a powerful header.
Here are the five things we learned from the clash at the Emirates.
Mourinho got his tactics wrong
In the build-up to the game Mourinho hinted that, with a Europa League semi-final second leg to come on Thursday, he would field several of the club's youngsters at the Emirates.
Given the Portuguese's record with youth players, that was always unlikely and so it proved when the line-ups were announced. Yes, Mourinho had made eight changes to the team that won at 1-0 at Celta Vigo but it was a starting XI filled with ten full internationals.
United began the game well, exploiting the space behind Arsenal's back three, but they retreated as the first half progressed and Juan Mata and Henrikh Mkhitaryan spent much of their time on the pitch as auxiliary wing-backs.
At times, United ended up playing a 6-3-1 system which meant when they did win back possession, Anthony Martial was their only option up front. It was easy for a shaky Arsenal defence to deal with.
Mourinho's side were too passive for much of the game and only the introduction of Jesse Lingard and Marcus Rashford livened up their attack. At that point, however, United were two goals behind and the game was gone.
Tuanzebe wasn't overawed
In the opening 45 minutes Tuanzebe completed 92.3 per cent of his passes, made two interceptions and completed every clearance he attempted.
He did give away possession cheaply in the second half on a couple of occasions but quickly made amends by winning the ball back and barging Sanchez to the ground.
By full time, Tuanzebe had won five of his seven tackles, made three interceptions, three clearances and two headed clearances. He proved that if Mourinho calls on him again this season, he is more than capable of performing.
Xhaka's inconsistencies remain
Wenger's reluctance to spend big money on players has been one of Arsenal fans' biggest gripes over the last decade.
He has, however, broken the the £30million mark on three occasions, signing Mesut Ozil, Sanchez and Xhaka.
The first two of that trio have justified their fee, even though Ozil has come under increased criticism this season. The Swiss international hasn't since arriving last summer.
There is little doubt Xhaka is a quality footballer, but in the first half against United he lost possession on five occasions and failed to complete a single tackle or interception. For a player whose primary role is to break up play, those stats are poor.
His goal in the second period was vital, yet lucky given the huge deflection. It did, however, settle Xhaka and he went on to complete 94.6 per cent of his passes attempted.
His lack of tackles completed – Xhaka failed in both he attempted – remains an issue though and his rashness has been punished this season with 11 yellow cards and two reds.
Until Xhaka sorts out his decision making when challenging for the ball, then Arsenal's midfield will never be as solid as it should be.
Welbeck slowly getting back to his best
The last two years have been cruel on Danny Welbeck. Two successive serious knee injuries have restricted the striker to just 16 starts in all competitions since April 2015.
The latest of those came against the club he spent 13 years with before leaving in 2014 for £16million.
But in the second period the 26-year-old was presented with a golden chance to score Arsenal's second and he took it clinically, powering a header past David De Gea.
In total, Welbeck had three shots on goal. One found the back of the net while the other two were blocked.
Danny Welbeck vs Man United:
? Games: 4
⚽️ Goals: 3
Dat Guy. ?? pic.twitter.com/b9GYouvXvw
— SPORF (@Sporf) May 7, 2017
The fixture has lost its lustre
Arsenal against Manchester United used to decide titles. Whenever the two sides met it would lead to create drama and controversy.
There was Pizzagate, the infamous row in the tunnel between Patrick Vieira and Roy Keane, and the way Gunners stars mercilessly mocked Ruud van Nistelrooy after he missed a late penalty in 2003.
This meeting between the two teams had none of that. It was tame. Even Mourinho and Wenger, two coaches who genuinely dislike each other, were civil for much of the contest.
Given both sides are outside of the top four, it's perhaps not surprising the match lacked the intensity of previous encounters. But Thierry Henry, an Arsenal legend who had countless tussles with United over the years, summed it up best.
He said: “This morning I was thinking that this is the first Arsenal against Man Utd game where my excitement is not there.”
Until both clubs are back near the top of the Premier League table, it's unlikely we'll see another decisive Arsenal – Man United clash anytime soon.