The 31-year-old's aerial dominance made it difficult for Swansea, but Pulis also took time to pay tribute to a resurgent Swansea in the second-half.
The Stoke manager told reporters: "I thought in the first half we were very good.
"The worst thing that happened was half-time - we came out very slow and sloppy in the second-half and Swansea controlled the play.
|VITAL HOME WIN - PULIS
|80/1||Peter Crouch is 80/1 with William Hill to finish as the Premier League's top-scorer
Kenwyne Jones replaced the former Tottenham striker with five minutes to play despite Crouch being on course for a hat-trick.
"I just wanted to give Kenwyne a bit of time, and the header against the crossbar - that should be food and drink for Peter," Pulis added.
"The scissors kick is a different thing - I'll speak to him on Monday about that. I can't afford for him to get injured!"
Crouch's performance impressed his manager and he believes the striker has done enough to be rewarded with a recall to the England side.
"I'm not reluctant [to talk about Crouch and England], but Roy [Hodgson] has a lot of experience and the last thing I want to do is tell him what team to pick.
"It has to be up to him. I don't think Peter can do any more than score goals and play well, and you have seen him today - in the first half he was unplayable."