Crouch's recent good form was evident in the 12th minute as a corner from Glenn Whelan provided the perfect opportunity for the England international to score with a trademark header.
Swansea could have equalised midway through the first half but Michu fired his shot wide of the goal after an impressive passing move from the visitors.
Crouch doubled his tally before the break after a goalmouth scramble ended with the ball falling to the feet of the opportunistic striker and he made no mistake from close range.
The Welsh club started the better of the two sides after the break and Ki Sung-Yueng was close to pulling a goal back but Asmir Begovic reacted superbly to tip the ball away from danger.
Swansea were denied a penalty midway through the second period when Ben Davies was challenged by Jonathan Walters but the referee was confident that it was a fair tackle.
Matthew Etherington looked dangerous after coming off the bench for Stoke and his cross nearly provided a third goal for the hosts but Crouch hit the crossbar with his header as his search for hat-trick ended in frustration.
Walters could have extended the size of Stoke's victory in the closing stages but his effort was easily stopped by Vorm as the Potters cruised to a comfortable win.