The win represented Louis van Gaal’s third victory, in three competitions, over the past six days, but more signficantly, damaged Arsene Wenger’s hopes of winning Arsenal’s first league title in 12 years.
The 18-year-old forward, who scored twice in the mid-week Europa League victory over FC Midtjylland, was on the mark again in an astonishing first half in which he beat Petr Cech on two occasions.
To make his impact all the more stunning, the goals came within three minutes of each other as United delivered a serious blow to Wenger’s aim of narrowing the five-point advantage that leaders Leicester City held before kick-off.
After 29 minutes, Ander Herrera started a move with a telling tackle on Theo Walcott, sparking a counter-attack that ended with Guillermo Varela crossing from the right and Gabriel hacking a poor clearance directly to Rashford.
The teenager did the rest with a composed finish from a dozen yards, the first shot of his Premier League career resulting in his first goal.
Arsenal’s poor defending was badly exposed in that attack and worse was to follow from the next serious foray into their territory with Varela again influential, making an important header that kept the ball in play.
Jesse Lingard received the ball and picked out Rashford, who had again slipped his marker Gabriel, and the youngster planted a perfect header past the diving Cech.
Wenger looked stunned on the Arsenal bench, a mood reflected by his players, although his side were able to pull an important goal back before the interval, predictably through the former United striker Danny Welbeck.
Mesut Ozil was the architect with an inch-perfect free-kick from midway inside the United half and Welbeck, who eluded his marker Marcos Rojo too easily, guided a header past David de Gea from 10 yards.
– Herrera on target –
The goals were the highlight of a thrilling first half in which Nacho Monreal should have given the visitors the lead after just seven minutes when he chased Ozil’s through-ball into the area and was denied well by De Gea.
Rashford won a free-kick inches outside the area after a trip by Gabriel, with Memphis Depay’s low set-piece being well held by Cech, while Alexis Sanchez replied for Arsenal with a snapshot that flew narrowly wide.
The entertainment continued after the restart as United sought to continue a remarkable run of close to 250 Premier League home games in which they have led at half-time and not lost.
Morgan Schneiderlin saw a shot blocked from a home corner and Cech needed two attempts to keep out Depay’s long-range shot as Arsenal toiled, prompting Wenger to bring on Olivier Giroud just after the hour in place of the ineffective Walcott.
But the next attack brought United a precious third goal, in the 65th minute, with Rashford again involved as he held up Juan Mata’s through ball before laying it back to Herrera just outside the area.
The Spanish midfielder’s crisp shot might have been saved by Cech, but a strong deflection off Laurent Koscielny gave the diving Arsenal goalkeeper no chance.
Again, Arsenal responded, from Sanchez’s right-wing cross on 69 minutes, which found Welbeck on the six-yard line for a shot that was blocked by De Gea.
The rebound fell kindly for Ozil, who showed predictably superb technique in keeping a bouncing ball down and driving it past the diving De Gea from 15 yards.
Herrera and Aaron Ramsey were cautioned for a scuffle as tempers became frayed and Van Gaal argued with the fourth official, throwing himself to the ground theatrically to make a point.
But apart from half-chances for Giroud and Kolscielny, both of whom missed with headers, there was little further goalmouth action.