Chelsea maintained their perfect start under Maurizio Sarri thanks to second-half goals from substitute Pedro and Eden Hazard.
Pedro opened the scoring with 20 minutes to play, after combining well with Olivier Giroud.
Following a smart one-two, he found a pocket of space on the edge of the box and fired low past former Blues keeper Asmir Begovic.
Hazard sealed the points with five minutes to go after breaking down the left and exchanging passes with Marcos Alonso.
From a tight angle, the Belgian drilled his shot under Begovic and into the net.
The win ensured Chelsea kept pressure on Liverpool, who sit top of the Premier League table.
Sarri’s side dominated possession throughout the match but struggled to create clear chances inside the first 70 minutes.
And for all of Chelsea’s early pressure, it was Bournemouth who had the better chances in the first half.
The first was gifted to them by David Luiz, who gave the ball away to Josh King on the halfway line.
The Cherries striker drove towards the box and squared to Ryan Frazer, but N’Golo Kante made a goal-saving challenge before he could get his shot away.
On the half-hour mark, Callum Wilson nearly gave the visitors a lead. Diego Rico curled an inviting cross into the box but it bounced off Wilson’s knee and over the bar from five yards.
The hosts themselves did come close moments before half-time.
After strong running from Kante, the ball fell to Hazard inside the box and he cut his pass back to Alonso, who fired against the post.
Pedro, who replaced Willian after 65 minutes, wasted little time in changing the game.
He could have had a brace after drilling a low shot at Begovic 10 minutes after breaking the deadlock.
Instead, it was Hazard who rounded off another solid display with his second goal in as many games, and Chelsea now has four wins in four under Sarri going into the international break.
