Chelsea made it four wins from four Premier League games under Maurizio Sarri after goals by substitute Pedro and Eden Hazard helped see off Bournemouth.
The Cherries had produced a stubborn defensive display to frustrate the hosts before Pedro struck seven minutes after replacing Willian.
The Spaniard exchanged passes with fellow substitute Olivier Giroud before his deflected finish beat former Blues keeper Asmir Begovic.
Hazard doubled the lead with a quality finish from an angle while Bournemouth’s ex-Chelsea defender Nathan Ake blazed over from three yards out when the game was goalless.
Blues dig deep to continue winning start
Chelsea are level on points with leaders Liverpool, who have a superior goal difference, but they had to dig deep against a resolute Bournemouth side, and once again the Blues left it late before their fans could bask in another victory.
Two weeks ago, their winner at home to Arsenal did not arrive until the 81st minute. At Newcastle last week, it was even later.
Against the Cherries, Hazard’s second goal – which ultimately sealed the points – came five minutes from time after Sarri’s side had dominated possession but struggled to break Bournemouth down until Pedro struck.
Marcos Alonso was denied by the post at the end of the first half, while the Spaniard was further frustrated by a fine save from Begovic, and it was only when Hazard notched his second goal in as many games that the hosts could finally relax.
Chelsea have won their first four games of the season for the first time since 2014-15, when they went on to win the Premier League.
Bigger tests lie ahead, but Chelsea have started strongly under Sarri and that bodes well for the future.
Positives in defeat for Cherries
This was Bournemouth’s first Premier League defeat since 28 April.
Having stunned Antonio Conte’s Chelsea 3-0 in the corresponding fixture last season, they were good value for a point until Pedro’s breakthrough after 72 minutes.
Eddie Howe gave Premier League debuts to £25m record signing Jefferson Lerma and Spanish full-back Diego Rico, and his side were hard-working as they frustrated Chelsea for long spells.
But they should have taken the lead, producing two glaring misses either side of the interval at 0-0, as Callum Wilson fired over from close range before Ake failed to hit the target from inside the six-yard box.
Despite defeat, the Cherries will go into the first international break of the season in good spirits, reamining sixth in the table after two wins and a draw from their opening four games.
In addition, they now face Leicester (home), Burnley (away), Crystal Palace (home), Watford (away), Southampton (home) and Fulham (away) before they face another major top-four contender – Manchester United at home on 3 November.