Stoke fell to their third consecutive defeat despite a stunning 65-yard goal from Charlie Adam.
Chelsea started brightly looking to find an early breakthrough, which nearly came in the second minute but Asmir Begovic clawed away Loïc Remy’s deflected effort.
The pressure told and Philipp Wollscheid fouled Cesc Fàbregas in the box, which gave Eden Hazard the opportunity to give the Blues the lead.
The Belgian duly obliged and stroked home from 12 yards sending Begovic the wrong way.
It was seemingly petering out to half-time until Adam received the ball and unleashed an effort from inside his own half. The ball flew over 6ft 6 goalkeeper Thibaut Courtois, who did manage to get a hand onto the ball but it wasn’t enough.
Jose Mourinho brought striker Diego Costa on after the interval but the Spain international only lasted 12 minutes after a reoccurrence of a hamstring injury that forced him off against Hull.
Chelsea won the match after forcing another Stoke error. Begovic attempted to roll the ball out to Steven N’Zonzi, who wasn’t ready to take possession, and Hazard pounced to take advantage by running through on goal before squaring to Remy to tap into the unguarded goal.
The Potters nearly fought back a few minutes later when N’Zonzi was allowed space and his strike from around 20 yards struck the post.
Juan Cuadrado came off the bench and forced Begovic into a magnificent double save to stop Chelsea from extended their lead.
In stoppage time Marko Arnautovic had the chance to find the equaliser but he lashed horribly wide after Chelsea failed to deal with Geoff Cameron’s long throw.
Chelsea extend their lead to seven points and still have a game in hand against Leicester while the Potters sit in tenth looking to better their ninth placed finish last season.
Chelsea: Courtois, Ivanovic, Cahill, Terry, Azpilicueta, Matic, Fabregas, Willian, Ocsar (Costa) (Drogba), Hazard, Remy (Cuadrado.)
Stoke: Begovic, Cameron, Shawcross, Wollscheid, Wilson, N’Zonzi, Whelan, Adam (Pieters), Ireland (Crouch), Diouf (Arnautovic),Walters.
Referee: Jon Moss