Results earlier in the day had presented Wolves with an opportunity to reduce the six-point gap between them and safety, but for the third successive match they took the lead only to end up with nothing.
Winger Michael Kightly put Wolves in front in the 26th minute with a lofted pass that drifted straight in, but Robert Huth drove home an equaliser with eight minutes of the first half remaining before Crouch nodded in the winner just after the hour mark.
The loss was the visitors' sixth in a row and with only six games left, things are looking increasingly bleak for Terry Connor's men, who have taken only one point from a possible 21 since he replaced Mick McCarthy as manager.
Stoke, meanwhile, are up to 11th having gone beyond the 40-point mark, the tally generally regarded as a guarantee of safety which their boss Tony Pulis had put great emphasis on all season.
Pulis wrote in his programme notes that he was not buying the talk that Wolves were already dead and buried, but he may have reconsidered that assessment by the final whistle.
Wanderers showed some pep in attack, but at the back - where they were without captain Roger Johnson, who had been dropped a week after his on-field confrontation with goalkeeper Wayne Hennessey - they looked worryingly vulnerable.
Jon Walters produced the game's first attempt on goal in the seventh minute but sent it over the bar from distance, and four minutes later Wolves' Stephen Ward tried an ambitious effort of his own which also sailed off target.
Another attack from the visitors saw Sylvan Ebanks-Blake strike from the edge of the box, but he did not make proper contact with the ball and it rolled through to Potters goalkeeper Asmir Begovic.
Stoke started to step things up and Walters was guilty of a terrible miss as he headed wide right in front of goal from Crouch's knock down.
The hosts were swiftly made to pay for that profligacy, with Kightly putting Wolves in front within three minutes.
He chipped the ball into the box and although Dave Edwards failed to connect at full stretch, his swing at the ball seemingly succeeded in putting off Begovic, who allowed it to go straight in.
Kightly then had an effort blocked, but the Potters looked to respond quickly and after Karl Henry - back as skipper in Johnson's absence - had cleared a Huth header off the line and Crouch struck wide, they drew level.
Wolves were unable to deal with a free-kick and the ball came to Ryan Shawcross, who teed up Huth to power in off Hennessey's legs.
Stoke kept up the pressure, with Hennessey catching Shawcross' attempted lob and saving Walters' header either side of a Marc Wilson shot that went over.
Wolves tried to get some momentum going at the start of the second half and won an early free-kick in a useful position which Steven Fletcher could only clip into Begovic's arms.
Kightly then made more of another, whipping in a cross which Sebastien Bassong nodded wide.
Matt Jarvis was next to send in a dangerous delivery which Stoke just got away, but Wanderers were soon behind as Crouch met Jermaine Pennant's free-kick with a header in the 61st minute that looped over Hennessey.
Wolves needed to react and Kightly burst forward with a mazy run, but Jarvis could not put his pass in at the far post.
Kightly tried to angle the ball towards goal but it flicked up off Glenn Whelan's head.
Connor threw on striker Kevin Doyle and the Republic of Ireland international brought a save out of Begovic, but the visitors had little else to offer and are now staring the prospect of relegation in the face.