The Red Devils couldn't have asked for a better start with Paul Pogba volleying home after 16 minutes, with a chance from Mkhitaryan and Ashley Young clattering the post making for a very entertaining first period.
The Gunners came flying out for the second period with Mkhitaryan scoring against his old side six minutes after the restart, United pushed as the minutes ticked down with Marcus Rashford having a goal disallowed but Fellaini made sure that Wenger's swansong in Manchester was one to forget.
Volleying home the opener
Before a ball was kicked a moment was taken to appreciate Wenger in his final appearance at the Theatre of Dreams, but when the attention turned to the pitch it was the Red Devils who took control early on and managed to take the lead after 16 minutes.
Romelu Lukaku did very well inside the area to dink the ball to the back post for former Gunner Alexis Sánchez but his effort was deflected onto the post by Héctor Bellerín, luckily for United the bounce was straight into the feet of Pogba who made no mistake by hitting it into an empty net.
Going very close
Despite going behind Arsenal didn't let up and came incredibly close to getting back in it just minutes after going behind, it was excellently set up with Ainsley Maitland-Niles' back-heel straight into the feet of Mkhitaryan but his effort whizzed just wide of David De Gea's far post.
United were inches away from adding a second four minutes from the break, Young did brilliantly to dance his way past Bellerín and put the cross in but it caught out David Ospina but he was saved his blushes by the woodwork.
Marking his return with a goal
Wenger will have been hoping to leave Manchester for the final time with something, and he was rewarded pretty early in the second period, and it would only be right that it was former Red Devil who got them back in it.
Granit Xhaka did well to win possession in the midfield and supply the ball through to Mkhitaryan, it was too easy for the Armenian as he rolled one through the legs of Victor Lindelöf and into the far corner.
Snatching right at the end
Many fans wouldn't have been unhappy to see the points shared to send Wenger out of the North West on a high, but United had different ideas as they threw the kitchen sink at it late on.
Anthony Martial sent in a great cross from the left which is met by Fellaini but his header comes back off the post, Rashford is there to steer in the rebound but the flag was raised for offside.
United continued to push and push and were rewarded a minute into time added on, Young curled in a great ball after the corner broke down and Fellaini leapt highest to head past a sprawling Ospina.