A virtuoso performance from David de Gea inspired United to victory over in-form Arsenal in a thrilling contest that will live long in the memory.
This was the Reds first win away to one of the other so called "big" clubs in the league under Mourinho, with United indebted throughout to the scarcely believable heroics of DDG - who cemented his status as undoubtedly the best keeper on the planet.
But there was a late blot on the copybook when the again impressive Paul Pogba was sent off 15 minutes from time for a late challenge on Hector Bellerin - a dismissal that will rule him out of next weekend's Manchester derby.
The Gunners were on a run of 12 successive wins at the Emirates, but the hosts were the architects of their own downfall as United went ahead in the fourth minute.
Laurent Koscielny's underhit backpass was collected by Valencia, who play a neat one-two with Pogba and slotted home through the legs of the advancing Petr Cech.
Seven minutes later, Arsenal were sloppy again and United made them pay with a wonderfully-crafted team goal.
Shkodran Mustafi dallied on the ball, Lingard nicked it off him and found Romelu Lukaku, whom in turn picked out Anthony Martial. The lively Frenchman cut inside and cut the ball back for Lingard, who had continued his run, and the in-form winger culminated the move when he swept the ball home off a post.
United looked capable of scoring from every attack, but De Gea was soon called into action as he palmed away Bellerin's dipping drive, saved well from Mesut Ozil and then knew little about a brilliant block from Alexandre Lacazette.
The Spaniard produced an even better save, however, on the stroke of half-time. Sanchez's inswinging free-kick ricocheted off Lukaku and changed direction, but Dave was equal to the effort and tipped it away from almost inside the line.
Lingard and Martial both went close in quick succession at the other end, but - four minutes after the interval - Arsenal got themselves a lifeline.
Sanchez linked up with Ramsey who burst through and found Lacazette - who was supposed to be ruled out with injury - and he fired in from close range.
Lingard and Martial twice went close in quick succession, but the Gunners came on strong and United again needed our keeper to come to the rescue. De Gea somehow saved one-handed to keep out Lacazette from two yards, before his quick reflexes denied Sanchez's point-blank follow-up with his foot.
The Reds re-established the two goal advantage in superb style three minutes after the hour mark. Lukaku released Lingard who found Pogba out wide and the midfielder held off Sead Kolasinac to find Lingard, who applied the finish from five yards.
Pogba's afternoon then turned bittersweet when he was sent off for a clash with Bellerin, before Arsenal substitute Danny Welbeck had a penalty appeal turned down.
United held firm in the closing stages for another crucial win and our first at Arsenal for three years.... now for the derby!
United Faithful Man of the Match: Three words. David. De . Gea
Overall team performance: 7.5/10