Ander Herrera had Manchester United on the brink of victory before Arsenal earned a 1-1 draw eight minutes from time at Old Trafford.
Ander Herrera's eighth goal of the season looked set to prove decisive as Louis van Gaal's men made Arsenal pay for a listless first-half display.
The visiting side improved significantly during the second period and, after injury forced United goalkeeper and reported Real Madrid target David de Gea from the field, Arsenal pulled level with eight minutes to play - Theo Walcott's strike taking a decisive deflection off fellow substitute Tyler Blackett.
The result means Arsenal remains two points above fourth-placed United in the Premier League and can avoid a potentially tricky Champions League play-off tie by beating relegation-threatened Sunderland in its midweek game in hand.
Manchester City is guaranteed a top-three finish following its 4-2 win over Swansea City earlier on Sunday.
Marcos Rojo and Radamel Falcao replaced injured duo Luke Shaw and Wayne Rooney for United, with Chris Smalling taking the captain's armband in the latter's absence.
An unchanged Arsenal failed to make much of an impression during a quiet opening to the game, Falcao enjoying the only opening of note when a fine challenge from Laurent Koscielny denied him on the end of Juan Mata's pass.
Mata struck a free kick from the edge of the area into David Ospina's arms before a mix-up between De Gea and Phil Jones almost presented Olivier Giroud with a chance to open the scoring.
The first goal fell United's way shortly afterwards in the 30th minute. Ashley Young sent in a searching cross from the left and Arsenal's defenders were drawn towards Marouane Fellaini, leaving Herrera with room to slam home a volley at the back post.
Smalling inadvertently blocked a drive from teammate Daley Blind as a lackluster Arsenal limped towards halftime.
Alexis Sanchez had been largely starved of service by the time he sliced wildly over from Giroud's flick on.
United continued to control the early second half play, with Mata to the fore.
The Spanish schemer was unable to create a goal for on-loan Monaco striker Falcao, who waved an apparent farewell to the Old Trafford faithful in United's final home game when he made way for Robin van Persie after the hour.
A De Gea departure would be harder for United supporters to stomach and the goalkeeper was serenaded from the terraces when he saved with his feet from Giroud.
With 20 minutes remaining, Aaron Ramsey was able to lift the ball over De Gea, but Rojo made up for losing the Arsenal midfielder's run by making a vital clearance.
A back injury ended De Gea's afternoon early, heralding a belated United debut for Victor Valdes.
And the former Barcelona man was beaten when Walcott collected a raking pass from the excellent Ramsey and his effort across goal spun in off Blackett.
Giroud then rippled the side netting as Arsenal pressed for the win with an urgency they badly lacked before halftime - although Van Persie almost caught his former team out when he lashed over in the 88th minute.