Arsene Wenger at last got his first competitive win over Jose Mourinho thanks to this 2-0 victory, and has thereby ended United's odd 25-game unbeaten league run which nearly certainly ended their chances of finishing in the top four, while energising their own.
But on Sunday, goals from Granit Xhaka and former United man Danny Welbeck saw Mourinho's side go down 2-0 to Arsenal.
Arsenal remains sixth, but can leapfrog fifth-placed United with victory at Southampton on Wednesday and have a further game in hand on third-placed Liverpool, who is seven points clear of them on 70.
The bigger picture for Arsenal is that they remain in contention for a top-four finish that may convince some of the doubters that Wenger is worth a new contract when his current deal expires at the end of the season.
Arsenal had to overcome early nerves against Manchester United but the 2-0 win was reward for their patience and eventual sharpness in front of goal, manager Arsene Wenger said.
Rooney forced Cech into action with a curling free kick from 25 yards after 65 minutes, but United were doing little to worry Arsenal as Wenger's side sat comfortably on their lead.
Mourinho made eight changes from Thursday's 1-0 win over Celta Vigo in the away leg of United's Europa League semi-final, notably awarding a full debut to 19-year-old defender Axel Tuanzebe.
Arsenal tested David De Gea soon after but the Spaniard easily saved an Alexis Sanchez effort.
Things soon settled down and Arsenal became the dominant force, troubling United twice just before the half-hour mark.
United have struggled to break into the Champions League qualification places all season, spending most of the campaign in fifth or sixth spot in the Premier League, and Sunday's loss leaves them in a hard position.
The Swiss global tried his luck from 30 yards out and it deflected off Ander Herrera and past De Gea to give Arsenal the lead.
And three minutes later, the hosts doubled their lead via a thumping header from Gunners forward Danny Welbeck.
But Arsenal continued to boss possession and United came no closer to reducing the arrears than a Rooney free-kick - one of several long-range efforts by the visiting skipper - that Cech turned behind.
Mourinho attempted to claw United back into the contest by introducing Jesse Lingard and Marcus Rashford from the bench, but neither had a huge impact.
"When you score you've got to be happy haven't you?"
And the 26-year-old has revealed why he refuses not to celebrate despite hit affiliation with Manchester United.