It took 72 minutes for the Blues to break the deadlock at Stamford Bridge. Pedro came off the bench to slot a fine finish past Asmir Begovic. Hazard then sealed the win with five minutes remaining.
"After the first half we talked together in the dressing room and said it was the kind of game where we need to be patient," Hazard said.
"When things are not good you need to be patient, you need to move the ball quick, like we did in the second half. Then when we have a chance we need to score and that's what we did.
"We have a lot of players who can score, Pedro did well and then we controlled the game so I think we deserved to win. A bit like Newcastle last week, it was a difficult game and Bournemouth defended well. We just need to keep the ball and move it quickly because in the first half we were a bit slower."