The England striker netted the 99th league goal of his career as Stoke achieved their first top-flight win at Molineux for 44 years at the 15th attempt.
Wolves went ahead through Stephen Hunt's penalty but an own goal from Kevin Doyle brought the Potters level after the break before Crouch decided the outcome.
The home side had been the better team in the opening 45 minutes, with winger Matt Jarvis causing plenty of problems and Karl Henry making his presence felt in midfield.
But they failed to capitalise on Hunt's spot-kick and Stoke were a transformed side in the second half, with winger Matthew Etherington and substitute Jermaine Pennant posing a threat.
Wolves made a promising start and the first effort at goal came from full-back Ronald Zubar following a Jarvis centre, but his shot curled just past the post.
Stoke defender Jonathan Woodgate became the first player to be yellow-carded for bringing down Jarvis in full flight, and was again to blame after 16 minutes when the recalled Hunt put Wolves ahead from the penalty spot.
Woodgate could have few complaints after chopping down dangerman Jarvis inside the box, although he escaped a second yellow card.
Up stepped Hunt to drill the spot-kick past Thomas Sorensen even though the keeper dived the right way.
Pulis decided a tactical change was needed and after 19 minutes replaced Woodgate with Pennant, allowing Ryan Shotton to drop back to right-back.
Hunt should have done better for Wolves when he headed too fiercely back across goal from a Jarvis cross with two players unmarked in the centre.
The Republic of Ireland international forced Sorensen to block his low drive from a narrow angle with his feet.
Jarvis switched to the right flank in place of Hunt but continued to cause problems.
Stoke's best chance of the first half fell to Etherington after Crouch dummied a centre from Shotton but he failed to make a full contact on his shot, which Hennessey collected.
Jonathan Walters had a good chance to level after 51 minutes when he found himself unmarked at the far post but Etherington's centre seemed to take him by surprise and he poked his effort wide.
Hunt was becoming more involved and forced Sorensen to save low to his left after being teed up on the edge of the box by Steven Fletcher.
But after 58 minutes an own goal from Doyle put Stoke level in fortuitous manner. Wolves skipper Roger Johnson was adjudged to have fouled Walters 30 yard out and Glenn Whelan rolled the free-kick into the path of Huth.
His free-kick took a major deflection off Doyle in the defensive wall and wrong-footed Hennessey, who got a hand to the ball but could not preventing it entering the net.
Dean Whitehead was booked for a challenge on Christophe Berra, who soon took retribution on the Stoke midfielder with a late tackle and was also yellow-carded.
Hennessey made a fine save to turn over a powerful 25-yard drive from Etherington but after 70 minutes, Crouch put Stoke in front.
Pennant turned the ball back into the path of Etherington whose deep cross was converted by Crouch, who got in front of left-back Stephen Ward on the far post.
Wolves substitute Sylvan Ebanks-Blake headed wide from a corner by Hunt but Stoke faced few alarms in the final stages before securing victory.