The hosts recorded their first victory of this Premier League campaign with a dominant performance, inspired by their tall striker who grabbed himself an excellent double
The striker was in top form, causing problems throughout the game against a shaky Swansea defence and grabbing his first goal in the 12th minute with a header after escaping the attentions of Chico Flores.
His second was a real poacher's goal as he latched onto a loose ball inside the penalty area in the 36th minute to double his tally at the second attempt.
Stoke City manager Tony Pulis named an unchanged side despite losing last time out to Chelsea, the Potters boss clearly impressed by the performance his charges put up at Stamford Bridge.
Michael Laudrup made three changes to his Swansea side that were beaten by Everton; Alan Tate was replaced by Chico in defence, Nathan Dyer was selected ahead of Wayne Routledge and Leon Britton returned in the centre of midfield in place of Jonathan De Guzman.
The home side began the stronger and gave Swansea very little time in possession with their midfield three pressing particularly high up the pitch.
Crouch was causing problems for the visiting defence right from the kick-off and after 12 minutes that threat was realised as the big striker opened the scoring with the simplest of headers from a Glenn Whelan corner. He escaped the attentions of the Swansea defence to meet the delivery from the left and head past Michel Vorm from six yards.
Swansea were really struggling to create chances, with only a 29th-minute Michu strike worthy of note, however, seven minutes later the home side doubled their lead and it was that man Crouch again.
The striker controlled a right-wing cross on his chest before knocking the ball down to Jonathan Walters, the Irishman beat Britton to the ball and Crouch latched onto the return to fire at goal. His first effort was saved by Vorm but he made no mistake with the rebound.
The visitors came out a much better side in the second half, presumably after a stern talking to by Laudrup during the break. There was much more of an attacking presence for them with Michu supporting Danny Graham better than he had done in the opening 45 minutes.
And they should have halved their deficit in the 66th minute but Graham was unable to convert an excellent chance. A corner from the right evaded everyone inside the six-yard box and fell to the feet of the Englishman at the back post. He steadied himself, worked the ball onto his right foot but skied his shot over the crossbar.
At the other end, Crouch very nearly had his third in the closing minutes of the game, but his back post header from a Matthew Etherington cross struck the top of the crossbar with Vorm well beaten.