The Clarets boss singled out his back four for plaudits after the game, and expressed his delight at the return of top goalscorer Danny Ings, who missed the previous five matches through injury.
"It was a team fighting for their lives and we had to be resilient and we knew our moment of quality would come in the end," he told BBC Sport.
"It was very professional from the players, especially in our shape and intensity throughout the game. Tom Heaton didn't have a shot to save and that was outstanding from the back four.
"I'm delighted that Danny Ings got 90 minutes and now we're just looking for the next game. I've told the players to be prepared and get ready for the next game."
The result leaves Burnley in second place in the table, with an 11-point lead over Derby County immediately below them.