The Gunners came into the game on an upswing after ending a run of three successive defeats with victory at Chelsea, while United were attempting to bounce back from a humiliating 4-0 loss at Liverpool.
And Arsenal took three crucial points as the visitors paid the price for shambolic defending and a missed penalty by Bruno Fernandes that undermined an enterprising attacking display.
Nuno Tavares put Arsenal in front after only three minutes following errors from Raphael Varane and Alex Telles, the defender turning in a simple finish after David de Gea saved Bukayo Saka’s shot.
Eddie Nketiah then had an effort ruled out by the video assistant referee for offside but after being called to look at his pitchside monitor the referee awarded a penalty for a foul by Telles on Saka immediately before Nketiah’s shot, and Saka converted from the spot.
United were a real danger in attack, the returning Cristiano Ronaldo deservedly pulling a goal back before the break for his 100th Premier League goal.
It set the scene for a United siege, only for Fernandes to waste their big chance by carelessly rolling a second-half spot-kick against the post after Tavares handled.
Arsenal cashed in on the reprieve when Granit Xhaka sealed the win by lashing home the Gunners’ third from 25 yards with 20 minutes remaining.
Arsenal’s win completed a superb response to three league losses that had jeopardised their top-four hopes.
Mikel Arteta’s side had to fight through adversity – they were not convincing defensively and had several escapes – but they seized their chances when they came to take full advantage of United’s carelessness in front of goal.
Tavares gave them the perfect start and while goalkeeper Aaron Ramsdale had a mixed afternoon, he also made some crucial saves, one from Telles early on and another from Diogo Dalot proving significant.
But Xhaka’s thumping drive gave De Gea no chance and there was a real mood of celebration inside Emirates Stadium at the final whistle.
Arsenal have inflicted serious damage on any slim hopes United may have had of reaching the top four while maintaining the pressure on north London rivals Tottenham in the battle to qualify for next season’s Champions League.