A Zlatan Ibrahimovic penalty deep into injury time rescued a scarcely deserved point for United against impressive Everton.
Phil Jagielka put the Toffees ahead in the first half as the Reds toiled for long periods.
Despite hitting the woodwork twice, United's 20-match unbeaten run looked to be over until Ashley Williams handled Luke Shaw's shot and Zlatan levelled things.
Zlatan and Ander Herrera both returned from suspension and the Swede went close early on, when he was thwarted by a superb lunging challenge from Williams.
Jesse Lingard flashed a shot wide and Marcus Rashford also went close but was flagged offside.
Ronald Koeman's side had barely threatened but grew into the contest and soon called David de Gea into action.
From the resultant corner, the visitors moved ahead as Jagielka stabbed home from close range from a Williams flick on.
That put the wind in Everton's sails and they almost doubled their lead straight away when Romelu Lukaku burst through but fired narrowly wide.
Joel Robles saved well from a Daley Blind free-kick and Herrera fired against the bar on the angle from the follow-up.
Herrera, along with Eric Bailly, was United's best player on the night and went close again, only to be denied by a superb sprawling save from Robles.
Ashley Young fired across goal and Rashford, lively as always, got himself into a good position but a brilliant challenge from Jagielka ensured Everton held on to their lead at the break.
Fit-again Paul Pogba was introduced at half-time and almost equalised on 54 minutes as United hit the woodwork for a second time.
After Rashford was fouled by Gareth Barry, Young's free-kick glanced off Lukaku and Pogba's header rebounded off the post.
De Gea saved well from a Barry header, and Maroaune Fellaini poked just wide of the post after he created space for himself.
Ibrahimovic thought he had equalised when he headed home a Herrera cross, only for assistant referee Scott Ledger to flag for offside, a decision which was marginal but correct.
Despite a sub-standard performance for long periods, United piled on the pressure in the closing stages as Everton determinedly clung to their slender lead.
Lingard's deflected effort flew inches wide, Marcos Rojo headed over and Ibrahimovic went close with a snapshot.
This side is nothing if not spirited though, and preserved the long unbeaten league run in dramatic style in the third minute of injury time.
Shaw's goalbound shot was handled by the stretching Williams, who was subsequently sent off, and Ibrahimovic kept his cool to slam home the spot-kick.
Overall team performance: 6/10
United Faithful Man of the Match: Eric Bailly. Classy and kept Lukaku quiet with an assured display.