Ander Herrera took advantage of some sloppy marking to hand Manchester United the lead but Theo Walcott's cross flew in off Tyler Blackett's leg and the match ended 1-1.
These two teams have engaged in some titanic battles over the years, but this was a very low-key meeting which will perhaps be remembered more for the goodbyes that took place, rather than the action on the pitch.
Radamel Falcao waved to all four corners of the ground when he was replaced in the second half
With a return of just four goals in 28 appearances, it seems unlikely the on-loan Colombian will be back next season.
And Real Madrid target David de Gea waved to the United fans as he came off with an injury in the second half and was replaced by Victor Valdes.
For United to snatch third place, they will have to beat Hull next weekend and hope Arsenal lose their final two league games against Sunderland and West Brom.
A fourth-place finish - and the Champions League play-off that comes with it - is almost certain for Louis van Gaal's team.
The match lived up to its low-key billing in the opening stages.
Falcao looked keen to impress - as he has done all season.
But the Colombian spent as much time on the floor as he did on his feet
Francis Coquelin, Laurent Koscielny and Nacho Monreal all muscled the striker off the ball early on.
The one time Falcao gained a yard on Koscielny, the Frenchman recovered to block the striker inside the box.
United's commitment could not be doubted
Ashley Young sprinted 50 yards to dispossess Alexis Sanchez, Antonio Valencia harried Monreal down the right and Herrera forced Santi Cazorla back into his own half.
But there was little for David Ospina to do
The Arsenal stopper's only save of note in the opening 15 minutes came when he collected Juan Mata's simple free-kick.
Arsenal offered precious little at the other end, though
It was only when Phil Jones slipped that they earned a sight at goal, but the centre-half recovered in a comical fashion, crawling on the floor and nodding the ball behind off Olivier Giroud's shin.
It was Arsenal's turn to perform some comical defending and hand United the lead
Monreal and Koscielny both followed Marouane Fellaini from Young's floated cross, which left Herrera free to volley in from close range.
United could have had a second in first-half stoppage-time thanks to more lax marking
Daley Blind, completely unmarked, flashed a curling shot towards goal from Juan Mata's corner, but captain for the day Chris Smalling accidentally blocked his team-mate's effort.
Arsenal continued to struggle immediately after the break
Alexis Sanchez volleyed well over the bar
Olivier Giroud fared much better, spinning Marcos Rojo in the box, but David de Gea rushed off his line to block.
The United fans responded by pleading with their star goalkeeper to stay.
Falcao bade what very much looked like a farewell to the United fans when he was substituted for Robin van Persie, waving to all four corners of the stadium as he walked off the pitch.
Aaron Ramsey beat De Gea for the first time, lifting the ball over the Spaniard after a brilliant ball from Sanchez, but Marcos Rojo put in a covering tackle.
What looked suspiciously like another goodbye came 15 minutes from time when De Gea hobbled off after pulling a muscle
The goalkeeper waved to the crowd as he walked down the tunnel
Valdes came on to make his United debut - 14 months after his last game for Barcelona.
The three-time Champions League winner was picking the ball out of the net eight minutes later.
Substitute Walcott peeled away down the right hand side and fired a low square ball across the box which flew in off Blackett's out-stretched leg.
Van Persie had a chance to snatch all three points, but ploughed his half-volley into the Stretford End at the death.
Source : PA
Source: PA