The Red Devils scored twice in 149 first-half seconds as Sanchez netted from a tight angle and Jesse Lingard scored from 12 yards out, both goals set up brilliantly by Romelu Lukaku.
Pierre-Emerick Aubameyang pulled one back to give Arsenal hope.
But Anthony Martial sealed the win when he scored from a rebound after Petr Cech parried Paul Pogba’s shot.
The Gunners lost centre-backs Sokratis Papastathopoulos and Laurent Koscielny to injury during the game.
Watch and download Arsenal Vs Man Utd Highlights (1 – 3) FA Cup 4th round below: –