Curbishley hauled off local favourite Mark Noble and winger Matthew Etherington in the 73rd minute as the fans sang "You don't what you're doing."
But Nolberto Solano and Luis Boa Morte were instrumental in the strikes that ended West Ham's three-match losing run in the Barclays Premier League.
Solano's 77th-minute shot from a Boa Morte cross hit a post and went in off goalkeeper Craig Gordon's legs before Boa Morte set up Craig Bellamy to make it 3-1 in added time.
Curbishley said: "We had to shake it up a bit because Roy Keane did ever so well in the second half, making changes to his team and they were a different proposition from the first.
"Some people didn't like it but that's football. One or two looked tired and I see that Mark Noble had pie and mash for lunch and perhaps it was two or three pies.
"He looked a bit leggy and he's got a sore foot as well but we had to change it.
"I think we deserved the win in the end and I'll certainly take the three points but Sunderland might feel hard done by. That's how it happens sometimes."
Sunderland manager Roy Keane was frustrated by his promoted side's latest failure to win away from home.
They were outplayed in the first half after Carlton Cole had put West Ham in front after nine minutes but looked likely winners after the break.
Keane admitted: "If you concede three goals like that you don't expect to win. The second goal was very unlucky but we had the ball a few seconds earlier and there are no excuses.
"I don't want to be talking hard-luck stories. We earned some plaudits for our performance at Arsenal, and probably today as well, but I just want to win matches and if you make mistakes in the Premier League you are punished. That's the beauty of it.
"Dwight Yorke picked up a thigh injury in training and we had to change the side but it wasn't working so I changed it again at half time.
"Kenwyne Jones still looks a very good signing for us. He's getting fitter and showing what he can do.
"The keeper's great save from him in the second half was a big moment but I don't want to talk about bad luck. I just take my hat off to the keeper."