Ollie Norburn's penalty in first-half stoppage time had given League One Shrewsbury the lead.
James McClean headed an early chance for Stoke over the bar before Ashley Williams drove wide from outside the penalty area.
Norburn had Shrewsbury's first effort when his shot from 20 yards was stopped by Adam Federici.
Tom Ince then went close for the Championship side when his shot was well kept out by Steve Arnold and then McClean volleyed off target.
Shrewsbury went ahead at the end of the first half when Aaron Amadi-Holloway was fouled in the box and Norburn kept his cool to convert from the penalty spot.
Amadi-Holloway had the chance to double the home side's advantage early in the second half when he headed Greg Docherty's cross over the bar.
Stoke manager Gary Rowett made a triple substitution and it paid off with a 78th-minute equaliser as Crouch volleyed home at the far post after Tyrese Campbell's cross fell his way.