Diego Costa looked to have secured his 50th Premier League goal in the 17th minute after swivelling and driving in Victor Moses' cross but the strike went down as an Adam Smith own goal after the ball deflected into the back of the net.
Chelsea took little time to double their advantage, however, as Eden Hazard ran on to N'Golo Kante's cross and coolly drove the ball past Artur Boruc in fine fashion just three minutes after the opener.
The hosts responded in the 42nd minute through Josh King, who fired a powerful effort in from the right although Chelsea were left fuming after seeing Smith's handball in the build-up to the goal go unpunished.
But Marcos Alonso put the game out of reach for the Cherries with his superb free kick in the 68th minute, which secured a 3-1 victory and keeps Chelsea's lead over second-placed Tottenham - who beat Watford 4-0 earlier on Saturday - at seven points.
Chelsea’s game with Bournemouth kicked off amid warm conditions on the coast, although the Blues’ back line had to deal with intense sunshine on their goal in the opening stages.
And the weather conditions nearly played a role in Bournemouth taking the lead just two minutes in when David Luiz attempted to clear Ryan Fraser's cross from the right, but instead skewed the ball toward his own net - which Thibaut Courtois leapt to save.
Chelsea recovered from the early threat to take the lead in the 17th minute when Moses - who had missed the last two games with a toe injury - crossed the ball into the area for Costa.
The striker swivelled and drove it toward goal where it took a deflection off Smith and flew past Boruc.
Despite his work for the goal, Costa was denied his 18th strike of the season - and also his 50th Premier League goal - with the effort going down as an own goal.
The Blues wasted little time to double their advantage just two minutes later when Hazard netted a fine effort from Kante's long-range pass over the top of the Bournemouth defence.
Both Kante and Hazard are contenders for the PFA Player of the Year award this season and, after seeing the way they linked up for Chelsea's second at the Vitality Stadium, it's easy to see why.
Kante's pass for the goal - his first Premier League assist for Chelsea - was accurate while the way Hazard ran around Boruc and coolly slotted in was impressive.
Despite going two up within 20 minutes, Chelsea appeared to take their foot off the gas and when Benik Afobe saw his volley hit the post, hit Courtois and then fly away from the goal, it was a huge let-off for Conte's side.
Costa, Pedro and Moses had further chances to put the game out of sight for the hosts but all three failed to convert their chances before Bournemouth were handed a lifeline three minutes before the break.
After referee Andre Marriner missed a handball from Smith as Alonso attempted to clear the ball, the Cherries launched a counter-attack in which Afobe found King with his pass from midfield before he unleashed a powerful effort that appeared to hit Luiz on its way into the goal.
The hosts returned from the break with a positive mindset following their late goal in the first half, and they could have restored parity through Fraser, who saw his fizzing effort fly wide of the post.
Costa then came close to putting the ball in the back of the net from Alonso's cross but the striker failed to sort his feet out in time and he ended up missing the chance to tap the ball in.
But the Blues didn't end up paying for Costa's somewhat lacklustre performance in front of goal as Alonso then handed Chelsea a 3-1 lead with his fine free kick in the 67th minute.
Costa won the set piece that resulted in Chelsea's third after being clipped by Cook, which Alonso drove over the Bournemouth defence and into the top right-hand corner of the net.
Moses could have then marked his return from injury in style but instead saw his goalbound effort blocked by Boruc, yet it didn't change the end result with Chelsea securing a 3-1 win that keeps the Blues on course for the Premier League title.