Stoke had taken a 30th minute lead through Carl Hoefkens and they did enough to win the game, but didn't reckon with Cardiff's leading scorer who notched his 22nd of the season.
The Bluebirds showed one change with Steve Thompson regaining his place up front from Warren Feeney, who was on the bench.
The Bluebirds had the better of the opening exchanges but it was not until the 10th minute that visitors' goalkeeper Steve Simonsen was tested by a Paul Parry shot.
The Potters almost caught Cardiff napping in the 19th minute when David Forde rushed out of his goal but missed the ball and Ricardo Fuller raced on but, when it was crossed back into the danger area, Chris Gunter slid in to clear.
Stoke took the lead slightly against the run of play when Vincent Pericard slipped the ball out wide to Hoefkens and he powered a right-footer across the diving Forde and into the far corner.
Dave Jones brought Willo Flood into the action on the hour but it had little effect in changing the course of the game as Stoke remained in command all over the park.
Chopra hit a free-kick straight at Simonsen in the 70th minute and then Thompson just failed to lob the visitors' keeper as Cardiff made a late attempt at finding an equaliser.
The visitors should have made the victory secure in the 80th minute when the busy Fuller laid on an open goal for substitute Martin Paterson, but he somehow side-footed wide from point-blank range.
With time running out Chopra bundled in to rescue a point for Cardiff, but it was not enough to keep their play-off hopes alive.