Wenger, presented with a gift by old rival Alex Ferguson before kick-off, rested the likes of Mesut Ozil and Alexandre Lacazette with an eye on Thursday's Europa League semi-final, naming his youngest league XI since 2011's infamous 8-2 loss at United.
And the Frenchman's young side were on track to do him proud, Henrikh Mkhitaryan levelling on his Old Trafford return after Paul Pogba's early opener for United.
But although United's attack was depleted by an injury that forced Romelu Lukaku off early in the second half, Jose Mourinho's men came up with a late winner.
Ashley Young's inswinging cross from the left was perfect for Fellaini to rise highest in the box to flick home the decisive goal in the second minute of added time.
A sixth successive defeat away from home in the Premier League will be irrelevant if Wenger can inspire a tunraround away to Atletico Madrid as United secured a top-four finish and tightened their grip on second place.
Pogba failed to take advantage of an early chance but he made amends with the opening goal in the 16th minute.
Lukaku floated a cross to the back post and, although Hector Bellerin deflected Sanchez's header on to the post, Pogba was well placed to knock in the rebound with a cushioned volley.
Like Sanchez, Mkhitaryan was facing the club he left in January, and the Armenia international almost levelled with a drilled strike that flew just wide.
Mkhitaryan and Maitland-Niles had penalty appeals rejected as United's intensity dropped, allowing Arsenal into the game, and Pierre-Emerick Aubameyang sent a poor header straight at David de Gea in the 36th minute.
Ashley Young's mishit cross rattled the post as United rallied at the end of the half, but the game had a strangely low-key feel, with little riding on the outcome.
Lukaku limped off early in the second half after taking a knock to his ankle and Mkhitaryan - who refused to celebrate - promptly levelled the scores in the 51st minute.
United allowed their former player too much space in midfield, Mkhitaryan finding the gap between Victor Lindelof's legs to beat De Gea from the edge of the penalty area.
1 - Henrikh Mkhitaryan is the first player to score for and against Manchester United in the same Premier League season. Devilish. pic.twitter.com/yATUJbWIgn— OptaJoe (@OptaJoe) April 29, 2018
A raft of second-half substitutions saw an already low tempo fall even further, although former United striker Danny Welbeck stung De Gea's palms with an ambitious strike from range and Fellaini rifled a drive over the crossbar.
United thought they had scored a late winner when Rashford bundled in on the line after Fellaini's header rebounded off the post, but the offside flag cut short their celebrations.
There was no stopping United in added time, though, Fellaini glancing in an excellent header from Young's perfect centre to ensure Wenger would only leave Old Trafford with his present from Ferguson.
Key Opta Facts:
- Manchester United completed a Premier League double over the Gunners for the first time since the 2011-12 campaign.
- Arsenal have lost six consecutive away league matches in the top-flight for the first time since January 1966, when they lost seven in a row.
- The Gunners are the only side in the top four tiers of English football yet to win a single point in an away league game in 2018 (P6 W0 D0 L6).
- Arsene Wenger lost his final match at Old Trafford as Arsenal boss – other than the Emirates and Highbury, he lost more matches at Old Trafford in all competitions as Arsenal manager than at any other ground (17).
- Manchester United have won all 10 of the Premier League games in which Paul Pogba has found the net – the only player with a better 100% record in the Premier League is Ryan Babel (11 games scored in, 11 won).
- Indeed, Pogba has now ended on the winning side in each of the last 18 league matches in which he has scored (10 for Man Utd, 8 for Juventus).
- This was Jose Mourinho’s 10th victory over Arsene Wenger in all competitions – the only managers he has beaten more often as a manager are Mark Hughes and Mauricio Pochettino (11 wins against both).
- Marouane Fellaini’s goal was the first 90th minute winner Manchester United have ever scored against Arsenal in the Premier League and the first in this fixture since January 2007, when Thierry Henry scored one at the Emirates in a 2-1 win for Arsenal.
- The average age of Arsenal’s starting XI for this game was just 24 years and 67 days, their youngest in a Premier League game since August 2011, which was also at Old Trafford against Man Utd (24y 65d); it was also the youngest line-up for a Premier League match this season.