Louis van Gaal’s side made the perfect start at Old Trafford thanks to Ander Herrera’s 30th-minute volley but they could not add to their lead despite being in the ascendancy for much of the opening 60 minutes.
The visitors threw on Theo Walcott and Jack Wilshere for the last 20 minutes and the move paid dividends seven minutes from time, Walcott’s cross deflecing off Blackett and past Victor Valdes to maintain the Gunners’ two-point lead over their hosts.
Manchester City’s win earlier in the day secured them a top-three spot finish but Arsenal, who face Sunderland on Wednesday, now need just two points from their last two games to secure a direct passage into the Champions League without the burden of the play-off round.
Despite their history of titanic battles, this was a low-key meeting which might be remembered more for
apparent goodbyes, misfiring Radamel Falcao waving to all four corners of the ground when he was replaced in the second half, before Real Madrid target David de Gea saluted the United fans as he came off with an injury to be replaced by Valdes.
In what was their final home game of the season, Manchester United started brightly and Arsenal needed Laurent Koscielny to make two crucial interventions from Ashley Young’s cross and Falcao’s shot.
It was clear to see Arsenal were trying to hit United on the break and the plan nearly worked in the 21st minute when Giroud got in behind a stumbling Phil Jones, only the England defender to head the ball against the Frenchman while scrambling on the floor.
Jones was living dangerously and he nearly had another calamity when his back-pass nearly caught out the onrushing De Gea and rolled into the path of Olivier Giroud, who would have had a tap-in had the Spaniard not got a boot to the ball.
Minutes later and it was all change in the mood around Old Trafford as the in-from Young turned Hector Bellerin inside out, before standing up a cross to the back post which Herrera volleyed into the back of the net.
Arsenal failed to manage a single shot in the first half – the first time in a single half of a Premier League match they had failed to do so since November 2004.
Arsene Wenger would have asked for a response from his players after the break and they gradually worked their way back into proceedings.
Giroud, who cut an isolated figure in the opening 45 minutes, flicked the ball into the path of Alexis Sanchez, but the Chilean could not direct his effort on target.
Van Gaal responded by sending for former Arsenal striker Robin van Persie and he replaced Falcao – a man who has managed just four goals in 28 appearances – with 30 minutes remaining.
However, it was Arsenal who were finishing the stronger and Mesut Ozil picked out Giroud, who turned his man at the near post, but could not beat De Gea.
Ramsey was next to go close for the visitors as he latched onto Sanchez’s through-ball. The Welshman lifted the ball over De Gea but he could not beat Marcos Rojo, who cleared the danger.
It was to be De Gea’s last involvement as Valdez came on for his Manchester United debut but it was not to be a happy one as he was picking the ball out of the net just minutes after entering the action.
With just seven minutes of normal time remaining, substitute Walcott broke down the right before his attempted cross deflected off Blackett to leave Valdes stranded.
It handed the Gunners their first Premier League point at Old Trafford in six years and it leaves them needing just two from their last two games to claim a first top-three finish since 2012 – Sunderland their visitors on Wednesday, live on Sky Sports.
Manchester United: De Gea (6), Valencia (6), Smalling (6), Jones (6), Rojo (6), Blind (6), Mata (6), Ander Herrera (7), Fellaini (6), Young (8), Falcao (6).
Subs used: Van Persie (5), Valdes (4), Blackett (5).
Arsenal: Ospina (6), Bellerin (5), Mertesacker (6), Koscielny (7), Monreal (6), Coquelin (6), Cazorla (5), Ramsey (7), Ozil (6), Sanchez (6), Giroud (6).
Subs used: Wilshere (5), Walcott (6), Flamini (5).
Man of the Match: Ashley Young