An exceptionally entertaining second half witnessed five goals as the Blues were twice made to retake the lead by a Potters side who gave them one of their toughest tests this season.
Gary Cahill gave Chelsea the lead when he headed in shortly before half-time, but Stoke defender Bruno Martins Indi levelled only a minute after the break when he poked in from close range.
Willian handed the Blues the advantage again only for Peter Crouch to level with a sidefoot effort high past Thibaut Courtois.
Stoke barely had time to celebrate, as moments after the restart Chelsea drove towards goal with Willian applying an fierce angled finish.
With five minutes remaining, the Blues all but sealed the three points when Diego Costa – who was magnificent as a target-man – shrugged off the attentions of Martins Indi to fire in the fourth.
Stoke were organised and disciplined at the back and threatened at the other end. In fact, until Cahill’s goal they were the better team and looked more likely to score first.
Their spirit was not broken even after Cahill’s opener, and seconds after the interval Martins Indi converted his first for the club from Crouch’s nod down.
Chelsea’s potent attack compensated for their failings at the back, and 11 minutes later Moses and Hazard combined before Willian poked in.
But yet again Stoke, who had not won a league game at Stamford Bridge since 1974, fought back. This time it was Crouch who got on the scoresheet in the league for the first time since May 2015 when he tucked home under pressure.
However, Conte’s Chelsea have shown great resolve this season. Just a minute after the second equaliser, Fabregas found Willian in the area and he rifled in from a tight angle.