Papiss Cisse gave the visitors the lead two minutes after half-time and it looked like Alan Pardew's team would end their miserable run of three straight Barclays Premier League defeats as the game headed into the final 10 minutes.
But in the 81st minute Cameron Jerome crossed for Jonathan Walters to head in, and four minutes later two substitutes combined as Kenwyne Jones set up Jerome for the winner.
Pulis said: "I've always got this thing in the back of my mind that when people say, 'Oh, he's made changes, he's been brilliant'.
"Why didn't I start with Michael Kightly, why didn't I start with Cameron? That's how brilliant I am.
"The lads have been fantastic, they've not played much this year but the spirit has been very good and their commitment to the group has been fantastic.
"They could easily have come on tonight and just jogged around and done what they wanted to do for themselves, but the effort they put in for the team was there for everybody to see, and that is a real plus for their character. And I think that really typifies what we've got at the football club."