Jon Walters put the hosts ahead with an eighth-minute breakaway goal, only for Didier Drogba to head an equaliser just past the half-hour.
The action became more frenetic in the second half with the Potters hitting the woodwork twice and forcing several good saves from Petr Cech, while Drogba was also denied by the crossbar late on.
A draw, coming after Manchester United had turned around a 2-0 deficit to beat West Ham earlier in the day, leaves Carlo Ancelotti's team 11 points behind the leaders.
Although they have a match in hand, there are only eight games remaining and it is difficult to see where the deficit will be made up in the final six weeks.
Chelsea's £50million striker Fernando Torres, dropped after nine matches for club and country without a goal, was given half an hour at the end but hardly threatened as his drought extended to 662 minutes since he last found the net, as a Liverpool player at Wolves in late January.
The omission of Branislav Ivanovic was more curious as his strength and aerial ability would have seemed ideal against the Potters.
Stoke won an early corner and the sight of Michael Essien marking Robert Huth, with eight goals this season, appeared a strange one which almost cost them when he headed Jermaine Pennant's corner over.
But it was speed over the ground - or lack of it - which proved Chelsea's undoing.
Walters took advantage of David Luiz's hesitancy out wide on the halfway line to nip past and race into the penalty area before cutting the ball back on to his right foot and beating Cech at his near post.
Chelsea's response saw Ashley Cole's diving header clawed away by Asmir Begovic and Florent Malouda volley just over from range.
But John Terry was almost embarrassed as much as his central defensive partner Luiz had been on the opposite flank when he lost possession to Kenwyne Jones before racing back to get in a crucial touch just as the striker looked to shoot.
Mistakes seemed very much the order of the day and Begovic was relieved to see Rory Delap clear after the goalkeeper dropped Frank Lampard's brilliant 25-yard volley at the feet of Nicolas Anelka.
With Jones giving Terry and Luiz a torrid time and Stoke's tigerish midfield snapping into challenges, it seemed Chelsea were being pushed out of the game.
But the one occasion the hosts failed to close down quickly cost them.
In the 33rd minute Anelka was given too much time from a deep position and he superbly picked out the diving Drogba to head powerfully past Begovic.
With Stoke's sheer tenacity and determination it was easy to see why they have scored 78% of their goals in the second half - the most in the top flight - and they continued to pressure their visitors.
Just after the restart both Walters and Jones dummied Matt Etherington's left-wing cross and Pennant drilled in a shot which Cech saved with his legs.
Drogba was even closer when teed up by Ramires on the right of the penalty area, his shot beating Begovic but hitting the outside of the far post, and the Potters goalkeeper was hardly convincing as he batted away a long-range Lampard drive.
Stoke rattled the crossbar twice within a few seconds as first Marc Wilson's free-kick crashed back off the woodwork, possibly as a result of Cech's touch, with Huth's header from the resulting corner only being kept out by the goalkeeper's outstretched hand and the frame of the goal.
Cech scrambled away a header from Etherington, Jones powerfully nodded wide and Pennant flashed a drive off target as Stoke looked more likely to score.
Drogba continued to pose Chelsea's greatest threat and he too was denied by the crossbar with a shot on turn.
Lampard had a claim for a penalty late on when Huth leant into his back as he bore down on goal, but referee Peter Walton saw nothing wrong.
In added time substitute Ricardo Fuller's header travelled the length of the goalline but dropped the wrong side of the far post.
A point was Stoke's first against their opponents since their promotion to the Premier League, and on balance they deserved more.