When Pedro made it 3-0 in the 23rd minute, it seemed any score was possible, but Chelsea did not find the net again until 17 minutes from time, when Willian picked himself up to score from the penalty spot after he had been felled by Geoff Cameron.
Davide Zappacosta rounded off the scoring in the 88th minute.
Blues boss Antonio Conte remarked: "I think our performance was very positive, we started the game very well with great desire to score early because, as I've said before, in this type of game if you score early it can become easier because your opponent has to change their plan.
"We started very well and we wanted that. I'm very pleased with the performance of all my players and to finish with another clean sheet. We are showing good solidity.
"We have to continue to work very hard to improve but to finish this year in this way is great for me, the club and the fans. It was a fantastic year for us because to win the title in England is not simple. To be able to do this with your first chance, I will remember this year forever."