Willian’s brace helped Chelsea edge an end-to-end game and match the top-flight record of 13 consecutive victories.
The Blues were twice pegged back by goals from Bruno Martins Indi and Peter Crouch during a frantic opening to the second half, as Stoke threatened to derail the Premier League leaders.
But Willian latched on to Cesc Fabregas’ pass and Diego Costa wrapped up the win late on to maintain Chelsea’s superb run.
Chelsea had the best chances of the first half, with Grant denying Costa and Eden Hazard before finally being beaten when Gary Cahill powered in a header from Cesc Fabregas’ cross.
But Stoke, who had looked a threat from set pieces, equalised after just 55 seconds of the second half.
Charlie Adam’s free-kick was nodded down by Crouch, who had got the better of Cahill, into the path of Bruno Martins Indi, who stabbed home.
After the initial shock, Chelsea created further chances with Willian firing just wide after good work from Victor Moses and Costa’s shot from a tight angle being saved by Grant.
They got their reward when Moses’ cross was touched off by Hazard into the path of Willian, who smashed the ball home.
Stoke, though, levelled again on 64 minutes, Crouch giving the Chelsea defence more problems before latching on to Martins Indi’s low ball.
But within a minute, the Blues were back in front as Fabregas threaded a ball into Willian’s path and the Brazilian finished with aplomb.
Costa blazed over the bar, after a quick counter initiated by Willian and Hazard, but he made the game safe late on as he shrugged off a weak Martins Indi before burying a shot.
Victory ensured Chelsea equalled the top-flight record of 13 consecutive wins in a single season, set by Preston and Sunderland in 1891-92 and Arsenal in 2001-02.
Chelsea: Courtois; Azpilicueta, David Luiz, Cahill; Moses (Ivanovic 82), Fabregas (Matic 73), Kante, Alonso; Willian (Chalobah 84), Costa, Hazard.
Subs not used: Begovic, Zouma, Loftus-Cheek, Batshuayi.
Marco van Ginkel signs new Chelsea deal
Chelsea midfielder Marco van Ginkel has signed a new contract keeping him at the club until 2019.
The Blues have also confirmed that the 24-year-old will spend the rest of the season on loan with PSV Eindhoven after he helped the Dutch outfit to the Eredivisie title during a loan spell last season.
Van Ginkel had originally been expected to return to PSV at the start of the season but suffered a knee injury and was forced to remain in London for his rehabilitation.
The Dutchman joined Chelsea in 2013 in an £8m deal from Vitesse, although he has only featured twice for the side in the Premier League as a substitute.
As well as his spell with PSV, Van Ginkel has also been farmed out to AC Milan and Stoke City.