The Potters took the lead at the Cardiff City Stadium on the stroke of half-time when Marko Arnautovic found the target from the penalty spot.
Kim Bo-Kyung was adjudged to have brought down Peter Odemwingie inside the box, and the 25-year-old made no mistake from 12 yards.
Peter Whittingham equalised for the Bluebirds six minutes into the second half with another spot-kick, and minutes later Juan Cala had an effort ruled out.
The result means that Cardiff remain stuck in the relegation zone, currently two points adrift of possible safety with only three games left.
On the other hand, Stoke can reflect on just one defeat in their last eight league matches.
Cardiff were unchanged from the team that won 1-0 at Southampton last Saturday, while Stoke boss Mark Hughes said same-again to the side that accounted for Newcastle United by an identical scoreline seven days ago.
The hosts started brightly in the sunshine as Mats Daehli saw a shot deflected wide and then Jordon Mutch forced Asmir Begovic to save low down, as they probed for an opening.
Daehli continued to be at the hub of Cardiff's most creative moments, with Mutch not far behind him. Stoke, in contrast, were content to play a patient passing game from the back, but home goalkeeper David Marshall remained untroubled.
Fraizer Campbell saw a shot deflected over the Stoke bar, but then Cardiff were forced to back-pedal as Stephen Ireland's pass was hit first time by Odemwingie and Marshall saved well.
Peter Crouch provided a predictable aerial threat to Cardiff's defence, yet the home side had more trouble keeping possession in their own half as Stoke began to pose serious threats through Ireland and Arnautovic.
There was an inevitable nervousness about Cardiff when they approached the final third, yet diminutive Daehli continued to tease Stoke defenders with his clever ball-control and distribution.
Cardiff then gained a free-kick just outside the Stoke box when Marc Wilson committed a foul, and Whittingham forced Begovic into a superb save as he palmed the ball wide.
It was Cardiff's best moment of the game, but they were stung in added time as Howard Webb ruled that Kim Bo-Kyung had fouled Odemwingie, and Arnautovic effortlessly struck the penalty past Marshall.
Odemwingie began the second period by collecting a yellow card following a reckless lunge at Cala from behind as Cardiff searched for greater urgency, and matters quickly deteriorated for Stoke.
Webb pointed the spot again just five minutes after the restart, this time for a Steven N'Zonzi foul on Campbell, and Whittingham drew Cardiff level to set up an incessant spell of pressure.
And it almost brought its reward as Cardiff captain Steve Caulker forced Begovic into a save low down, before the ball rebounded off the post and Cala headed in from an offside position.
It was comfortably Cardiff's best period of the game, but Stoke successfully manned the barricades before finally breaking out of their own half as they looked to subdue a vociferous home crowd.
Solskjaer then sent on ex-Stoke striker Kenwyne Jones 10 minutes from time - he moved to Cardiff in a swap deal with Odemwingie earlier this season - in the quest for a final push.
Stoke were content to play out the draw, although Odemwingie tested Marshall with a shot from outside the penalty area and the home goalkeeper also thwarted Stoke substitute Oussama Assaidi before Webb called time on the contest.