Nedum Onuoha, Asamoah Gyan and Danny Welbeck scored the goals for the Black Cats.
Sunderland managed to bounce back from the 5-1 loss to rivals Newcastle a fortnight ago.
Bruce told Sky Sports: “Two weeks ago we were hung, drawn and quartered. We were looking for a response and got it. They have worked very hard to get over the Newcastle defeat.
“It was the worst performance of my career two weeks ago and today was arguably the best. Today we have done okay.
“That’s management, the ups and downs are pretty horrific.”
