Cesc Fabregas set up Pedro to break the deadlock with a deflected shot that looped into the top corner.

Eden Hazard capped an impressive display by making it 2-0 from the spot after he was brought down by Simon Francis.

Chelsea added a third goal deep in injury time when Pedro's shot hit Steve Cook and the ball span over the line.

Bournemouth's best chance saw substitute Benik Afobe denied by Thibaut Courtois but the Cherries ended up well beaten.

Liverpool can reduce Chelsea's lead to six points if they beat Stoke on Tuesday.

Chelsea were missing two key components of their recent run, with striker Diego Costa and midfielder N'Golo Kante both suspended, but it made little difference.

Without Costa to lead the line, and the Blues £33m Belgium striker Michy Batshuayi again left on the bench, Antonio Conte went with a front three of Hazard, Willian and Pedro.

It took time for them to hit their stride but the three players eventually proved an effective combination.

They were happy to swap positions throughout the game but all three caused the Cherries problems when they ran at them, especially on the break.

"This is the first time we played without a real forward," Chelsea manager Conte explained.

"We tried this in training and I think for us at the moment this situation is the best, but I don't forget Michy because he is a young player with great talent. He is adapting to this league and its football. In the future, I trust in him."

Kante's absence, meanwhile, saw Fabregas recalled to partner Nemanja Matic at the heart of Antonio Conte's midfield.

Again they took time to settle down, giving Jack Wilshere too much room on a couple of occasions before the break, but they were far more assured after half-time.

Bournemouth boss Eddie Howe switched to a 3-4-3 formation to match Chelsea's shape and, initially, it worked.

Even when Pedro put the hosts ahead, the Cherries looked capable of causing them problems and Wilshere got on the ball in some good positions, going close twice.

It did not last, and Bournemouth were kept at arm's length for much of the second half - enjoying more possession than Chelsea but unable to do much with the ball, and in constant danger from counter-attacks.

"You can't be too upbeat about getting beaten 3-0 but there were fine margins and many elements of our game-plan worked," Howe said afterwards.

"They scored their first goal out of the blue, without any real sustained period of pressure, and the second goal just after half-time was the decisive moment."

Howe's side remain seven points above the relegation zone so have breathing space, but their away form is becoming a cause for concern.

"Chelsea look so strong in every department, so confident in every department. The win was without two of their biggest hitters - N'Golo Kante and Diego Costa. Once they got that first goal it was just a matter of how many.

"Their one-touch and two-touch play was just brilliant at times. Eden Hazard is in such incredible form and Willian had a fantastic game. Chelsea are red, red hot at the moment."

Match stats - Conte's fast start continues

Antonio Conte is the first Premier League manager to win 15 of his first 18 games in the competition

Bournemouth have lost three of their past four Premier League games, conceding three goals in each defeat

Eden Hazard is the sixth player to score 50 Premier League goals for Chelsea after Frank Lampard, Didier Drogba, Jimmy Floyd Hasselbaink, Gianfranco Zola and Eidur Gudjohnsen

Only Hasselbaink (84), Drogba (106) and Gudjohnsen (153) reached 50 Premier League goals for Chelsea in fewer games than Hazard (155)

Cesc Fabregas has provided 98 assists in the Premier League; only Wayne Rooney (101), Frank Lampard (102) and Ryan Giggs (162) have more in the competition's history

What next?

The Cherries have won only one of their nine games on the road this season, but have a chance to put that right on New Year's Eve when they travel to struggling Swansea.

Chelsea host Stoke on the same day, looking to move closer to Arsenal's record of 14 successive Premier League wins, set across the 2001-02 and 2002-03 seasons.

"To win 12 games in a row is not easy in this league," added Conte. "It's a fantastic run but it's important to continue that now.

"In four days we have another tough game and we have to prepare very well. Because now every team wants to beat you."

(BBC)