Mason Greenwood scored 13 minutes from time to salvage a 1-1 draw for Manchester United and deny Everton caretaker boss Duncan Ferguson a second consecutive Premier League victory.
United went into the game hoping to claim a third consecutive league win for the first time since January but David de Gea's failure to clear a first-half corner led to Victor Lindelof putting through his own net.
Everton defended resolutely as they sought to build on their 3-1 victory over Chelsea at Goodison Park, and the commitment shown by a side lacking a number of key players will raise inevitable questions about Ferguson taking the manager's job on a permanent basis.
But United substitute Greenwood produced the cutting edge in attack that the hosts had been lacking and his strike ensured Ole Gunnar Solskjaer's men extended their unbeaten streak to six league matches.
Jesse Lingard dragged a shot wide on the turn from eight yards after United swept forward from the kick-off.
Marcus Rashford and Daniel James both went close, feeding on incisive long passes Lindelof and Scott McTominay, before Jordan Pickford parried a dipping Rashford free-kick away from danger as Everton continued to come under pressure.
Without the pace to hit United on the counter-attack, the visitors took a more patient approach and were rewarded when Leighton Baines' corner was misjudged by De Gea and the ball grazed the goalkeeper's knuckles before bouncing off Lindelof's leg and into the unguarded net.
Luke Shaw surged down the United left after an hour and fired a powerful drive that Pickford did well to parry away, and nine minutes later Lindelof curled a shot over the crossbar from the edge of the box with Everton pinned back.
United's late pressure paid off when James found Greenwood on the edge of the box and the teenager tucked a low drive into the bottom corner of Pickford's net to spare United's blushes.
What does it mean? Low press remains a problem for Solskjaer
Manchester City's open, attacking play created space for United to play in when they won the derby, but Everton's packed rearguard proved trickier for Rashford and James to unpick until Greenwood's intervention.
Meanwhile, Solskjaer still cannot rely on the composure of a defence that has conceded in 12 consecutive league games – the first time United have done so since 1971.
Holgate and Davies fill the gap
With Gylfi Sigurdsson and Djibril Sidibe falling ill before the game, responsibility in the middle of Everton's midfield fell to Tom Davies and Mason Holgate, who coped admirably in protecting the back four and breaking up play.
Lacklustre Lingard highlights Pogba absence
Neither Juan Mata nor Lingard have made convincing claims to be United's first-choice attacking midfielder in Paul Pogba's enforced absence this season, and the latter was too often a bystander here while his team-mates struggling to turn the game.
After Colchester United visit Old Trafford in the League Cup on Wednesday, Manchester United travel to Watford in the Premier League while Everton entertain Leicester City in the cup and Arsenal in the league.