Alexandre Lacazette opened the scoring after a delightful team move that involved Aaron Ramsdale, Ben White, Takehiro Tomiyasu, Martin Odegaard and Bukayo Saka before a neat finish from the Frenchman.
Six minutes later, Odegaard notched the hosts second with a header from close range after Kieran Tierney headed the ball back into danger.
Gabriel put the result beyond any doubt just after the hour as the Brazilian rose highest to nod home from a corner.
The win takes the Gunners into fifth place for the time being, though United could leapfrog them once again with a win over Norwich in the evening kick-off.
Arch-rivals Tottenham sit just two points behind, though do have the advantage of having played two games less than their north London neighbours.