Arsenal had not beaten any of their current big four rivals, Chelsea, United or Manchester City, for 18 months but helped by the fifth-minute sending off of Dedryck Boyata they triumphed 3-0 at Eastlands.
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Earlier, United ended a run of four successive away draws with two goals for Wayne Rooney's stand-in Javier Hernandez in their dramatic late 2-1 win at Stoke City.
Liverpool, normally challenging those sides for a Champions League slot, remain in the bottom three despite claiming their second win of the season when Fernando Torres's first goal since August secured a 2-1 Anfield win over Blackburn Rovers.
One of his passes, into the path of Marouane Chamakh, produced Boyata's mad moment with a rash trip outside the box.
"We played some outstanding football at times and it's very difficult to stop a team playing at that tempo," Fabregas told Sky Sports.
"Even if they had 15 (players) and we had 11 we would still go and win."
"We never give in, we actually started to play after we lost the goal," said United manager Alex Ferguson.
"It's really difficult here as they really compete for everything. We got a bit careless but we managed to up our game just enough to get thro
