Andre Schurrle gave the visitors the lead after 10 minutes, but they could not extend their advantage despite having several opportunities to do so, with Ramires particularly culpable.
Chelsea paid the price when poor defending allowed Peter Crouch to equalise three minutes before half-time, and substitute Stephen Ireland put Stoke ahead five minutes after the break.
Schurrle struck again within three minutes to level things up, and it looked set to finish all square until substitute Oussama Assaidi unleashed a superb drive into the top corner in the 90th minute to earn Stoke victory.
Jose Mourinho compared the first half to those in Chelsea's other Barclays Premier League defeats of the season, against Everton and Newcastle.
He said: "I could see that result happening because after half an hour we should have been winning three or four nil, and we weren't.
"The three players behind the striker were playing so well, creating so much, but you have to kill the game. Normally you kill the game, but we didn't.
"I can compare this first half with another two first halves - Everton and Newcastle, they were exactly the same. In the last 15 or 20 minutes we didn't play well, the game they wanted was the game we gave them."
Liverpool won 4-1 against 10-man West Ham at Anfield as they moved past Chelsea into second in a match that featured three own goals.
Guy Demel was unfortunate to gift the hosts the lead just before the break before Mamadou Sakho and Luis Suarez netted either side of Martin Skrtel's blunder which pulled one back for the London outfit.
Joey O'Brien then sent the ball into his own net to complete the scoring in the match after Kevin Nolan had been sent off in the 83rd minute.
Pablo Osvaldo cancelled out Sergio Aguero's opener to end Manchester City's four-match winning run as Manuel Pellegrini's side were held to a 1-1 draw against Southampton at St Mary's, dropping the visitors down to fourth.
New manager Tony Pulis recorded his second win in charge of Crystal Palace following Tuesday night's victory over West Ham as they saw off Cardiff 2-0 at Selhurst Park.
Cameron Jerome's early header put them ahead before Marouane Chamakh netted his second goal in two matches to move Palace up to 18th.
Norwich bounced back from their midweek thrashing at Anfield as goals from Gary Hooper and Leroy Fer earned them a valuable win over West Brom at The Hawthorns.
In the evening match, another own goal - this time for Sunderland's John O'Shea - condemned the league's bottom side to a demoralising home defeat as Tottenham earned under-fire manager Andre Villas-Boas a second successive victory.
Defeat was all the more galling as the home side, just as they did against Chelsea in midweek, took the lead when Adam Johnson capitalised on keeper Hugo Lloris' blunder. However, Paulinho levelled within six minutes and Tottenham never looked back.