Wenger, warmly applauded by the home fans before kickoff, made eight changes from the side that drew with Atletico Madrid in the Europa League on Thursday as he looked ahead to the second leg next week.
The manager, fielding the youngest Arsenal side at Old Trafford since the one thrashed 8-2 in 2011, opted to give a debut to 20-year-old defender Konstantinos Mavropanos.
The Gunners had an early scare when, after a deflected cross from their former star Alexis Sanchez was cleared, the ball broke to Paul Pogba only for the France international to skew wide.
Back came the visitors, Henrikh Mkhitaryan having a low cross cleared and Hector Bellerin seeing another claimed by David De Gea before a Jesse Lingard centre was cut out at the other end.
United were beginning to enjoy the bulk of possession as the 15-minute mark arrived, but Arsenal's Reiss Nelson did his best to provide some spark when his low shot was held by De Gea.
But a minute later that spark arrived for United, Pogba playing the ball to Romelu Lukaku, whose cross led to Sanchez being denied when Bellerin diverted his header against the post only for Pogba to slam in the rebound.
Mkhitaryan drilled an angled strike just wide after being found by a deft Ainsley Maitland-Niles backheel inside the area as Arsenal came within inches of an equaliser.
Both Mkhitarayan and Maitland-Niles then went down inside the area in quick succession, the latter under challenge from Sanchez, but referee Kevin Friend was not interested in giving a penalty on either occasion.
Lingard raided forward but saw his ambitious shot blocked when he had Antonio Valencia available on the right, and when Valencia crossed towards Sanchez moments later the ball was just too high.
Pierre-Emerick Aubameyang had a chance as a relatively uneventful opening half approached its final 10 minutes, but there was no conviction in his header and the ball bounced through to De Gea.
Ashley Young then almost added an extraordinary second for Jose Mourinho's United when his cross crashed off the outside of the post with keeper David Ospina struggling to get across.
In the closing moments of the first half Aubameyang nearly turned provider, his cross from the right headed wide by Nelson, but the half-time mark arrived with United still 1-0 ahead.
Maitland-Niles threatened to burst through the centre for Arsenal as the second half got under way but was closed down and the ball ran through to De Gea.
Moments later, United had a problem as Lukaku was left limping after a challenge from deubtant Mavropanos and Marcus Rashford replaced him.
They had an ever bigger problem after 51 minutes as Arsenal equalised, former United man Mkhiatrayan played in by Granit Xhaka, who had won the ball back, and firing low past De Gea and into the corner.
Young's shot deflected behind for a corner as United tried to hit before Mkhitaryan tried his luck again, twisting into space inside the area but sending his finish over the top.
Shortly after the hour both managers made changes, Wenger bringing on Danny Welbeck for Nelson and Nacho Monreal for Sead Kolasinac, who had taken a knock, and Lingard and Ander Herrera making way for Anthony Martial and Marouane Fellaini for United.
Welbeck tried his luck from 25 yards after winning the ball from a dawdling Fellaini, but De Gea held the strike, and then Martial's cross towards Fellaini was well cleared by Mavropanos.
Chris Smalling, forward for a set piece, missed his kick as the ball was played back across the area, with Fellaini hooking over from the edge of the box as United began to step up the pace in search of the goal that would restore their lead.
Arsenal keeper Ospina went down in pain after a collision with Fellaini as the pair challenged for a cross but was able to continue after treatment and Arsenal made another change, Mkhitaryan making way for Joe Willock as the game entered its final quarter of an hour.
Fellaini just failed to get his head to a dangerous cross from the right, appealing in vain that he had been impeded, and Rashford touched home at the far post in the 90th minute only to be thwarted by an offside flag.
But Mourinho's men found a way to win, Young's cross headed past Ospina by Fellaini in the first of four added minutes.