Chelsea were three up at half-time as a sensational Danny Drinkwater volley came between goals from Antonio Rudiger and Pedro, both laid on by the brilliant Willian.
Willian then turned scorer in the second half by earning a penalty and then converting it before substitute Davide Zappacosta added a fifth late on.
Victory means Chelsea reduce the gap behind Manchester City to 13 points, with City facing Crystal Palace on Sunday, while Stoke stay two points above the relegation zone.
Simon Johnson assesses the key talking points at Stamford Bridge...
Alvaro Morata needs to improve his finishing on the deck
The statistics show that Morata has scored more goals with his head for Chelsea this season than his feet. It is not a surprise given the contrast in confidence the Spaniard displays when the ball is in the air to when it is at his feet. Every time the ball has been crossed high into the box, there seems no doubt in the 25-year-old's mind. He's usually put chances away with aplomb, as the seven headed goals suggest. Where Morata lets himself down is with his feet. At the moment he has struck just four times, but he's had numerous opportunities this term to improve that figure. There were a few examples against Stoke this afternoon, one in particular when he was sent clean through by Willian. However he didn't look convincing as he ran toward Stoke's goal and Jack Butland saved with ease. History repeated itself after the break and again Butland had little difficulty deflecting the ball to safety. Morata has made a positive contribution since joining from Real Madrid, but Chelsea need him to become more clinical to end the season with silverware.
Gareth Southgate given a reminder by Danny Drinkwater
It is unlikely Drinkwater will get taken to the World Cup next summer, but this display may at least give England coach Southgate cause for thought. Drinkwater's last appearance for the national side was in May 2016 and he has missed a few internationals since then due to injury or personal reasons. He rejected Southgate's late call in November to join up as he didn't consider himself fit enough, especially after aggravating a calf problem. That response was met with heavy criticism in the media and Southgate intimated that he was unlikely to give anyone new a chance when the next friendlies take place in March. But Drinkwater, who joined Chelsea from Leicester for £35m in the summer, showed against Stoke just what a useful asset he can be. His first goal for the Blues - a superb shot into the top corner - was noteworthy enough. However, his passing in the absence of Cesc Fabregas, was just as impressive.
If Chelsea do lose Thibaut Courtois, Jack Butland will be a good replacement
That may sound strange after the Stoke keeper conceded five goals this afternoon, but it could have been double that without him. There is still a lot of speculation surrounding Courtois' future, with his contract expiring in 18 months' time. Chelsea remain confident that he will sign an extension, yet Real Madrid continue to be linked to his signature. Should the worst case scenario happens, Butland is one of the keeper's Chelsea have monitored to step in. The 24-year-old is in contention to be England's No1 for the World Cup and his shot-stopping ability shows why. He has the right temperament to handle the big occasion too, something the Chelsea hierarchy would have noticed today.
Antonio Rudiger quietly proving his worth
The German international was one of the less heralded summer signings in the Premier League when he moved to Chelsea from Roma for £29m in July. Coach Antonio Conte has eased him into the first team gently, not hesitating to leave him on the bench. Still as 2017 comes to a close, Rudiger has made 19 starts in all competitions and is becoming more comfortable in a Chelsea shirt. This was the fourth successive time Rudiger has been in the first XI over the busy Christmas period and he helped Conte's side get off to the perfect start with a fine header inside three minutes. Rudiger is becoming popular with the Chelsea fans too, as the roars of approval whenever he made a timely intervention showed.
Chelsea enjoying their home comforts
The campaign didn't get off to the best of starts for Chelsea at Stamford Bridge, but things are on the up again now they've made it a lucky seven in west London. One of the reasons Manchester City were able to open up a gap over the champions early on was because of Chelsea's struggles on their own soil. An opening day loss to Burnley was soon followed by a draw against Arsenal and then a costly defeat to the now runaway League leaders. But Chelsea have recovered their mojo to make it seven wins in a row here and the team look more like their old selves in front of their own fans. It's come too late to challenge for top spot, but this form will help their bid to finish the best of the rest.
