Jonny Evans saluted the character United showed in registering a first domestic win at Stamford Bridge since 2002.
The Reds stormed into a two-goal lead, then won through Javier Hernandez's late tap-in after Chelsea - who also lost two players to red cards - had restored parity.
Now just a point behind the Barclays Premier League leaders, United demonstrated requisite fortitude - particularly as the Blues fought back from two goals down.
"I think that's probably the hardest game we've had this season, especially towards the end of the first half," the defender told Sky Sports. "Chelsea really came at us and put the pressure on us. It was a tough game and we were probably lucky to see it out to 2-1 at half-time.
"Going in 2-1 up was great because it was a bit of an onslaught at that stage, but you've got to show character in games like this. We came out for the second half and you've got to stand up coming here to Stamford Bridge.
"It's a tough game, we knew we were going to be under pressure. They got the equaliser and obviously the sending offs are in-between that, and we managed to finish the game off in the end."
Evans played a central role in the game's second sending off. Fernando Torres, booked for an earlier lunge on Tom Cleverley, tumbled under the defender's challenge and picked up a decisive second caution.
Though Chelsea animatedly protested the decision, Evans concluded that referee Mark Clattenburg had ultimately made the right call - despite admitting he had brushed the Spaniard.
"At the time I didn't feel like I'd made contact," he said. "I've seen it again and there was a bit of contact but I didn't feel like it was enough to