United reignited their Premier League challenge and dented Arsenal's title hopes with a thrilling victory inspired by 18-year-old Marcus Rashford.
The young striker repeated his European heroics with two goals in three first half minutes before ex Red Danny Welbeck pulled one back for the Gunners before the interval.
Rashford set up Ander Herrera to make it 3-1, Mesut Ozil ensured an nervy finale but a youthful United side held out for a hugely important win.
Arsenal had started well and went close through Nacho Monreal in the sixth minute, but the returning David De Gea kept out the full-back with a smart block.
The Spaniard's opposite number Petr Cech saved well from a Memphis free-kick, but the stopper proved powerless to prevent another magic moment from Rashford shortly before the half hour.
United broke forward and Juan Mata found the excellent Guillermo Varela on the right, Arsenal failed to clear the young full back's delivery and Rashford calmly fired home his finish from close range.
Arsenal were still reeling from that setback when they fell further behind, with three of United's Academy graduates again involved in the goal.
Varela picked out Jesse Lingard whom in turn crossed for Rashford to head home past Cech and send Old Trafford euphoric with joy.
The Gunners weren't going down easily, though, and the visitors gained a vital foothold in the match five minutes before half-time as Welbeck nodded in an Ozil free-kick to cap a frantic first 45.
Arsenal started the second half as they had ended the first- on the front foot and went close to a leveller through Alexis Sanchez whom had an effort repelled by the returning Marcos Rojo.
18-year-old Timothy Fosu-Mensah replaced Rojo for a United debut soon after but the Reds continued to carve out chances and re-established the two goal buffer on 65 minutes.
Rashford picked up the ball on the right and teed up Herrera whom thumped home from 25 yards with the aid of a deflected off Laurent Koscielny.
Memphis went close to a fourth but the Gunners responded quickly and halved the deficit once again when Welbeck forced a super save from De Gea but Ozil volleyed the rebound in off the turf.
Substitute Olivier Giroud headed over the bar in a spell of late pressure from the visitors but no further drama was forthcoming as United held out despite five added minutes.
Overall team performance: 8/10
United Faithful Man of the Match: Marcus Rashford. Scored twice and set up the other on a dream league debut.