Walters scored two own goals and missed a penalty in Saturday's game but he netted twice on his return to the Britannia Stadium, after Glenn Murray's 87th-minute penalty for the Eagles cancelled out Kenwyne Jones' opener.
Cameron Jerome claimed a late fourth for Stoke, who will tackle Premier League champions Manchester City for a place in round five in what is a repeat of the 2011 final which City won.
Pulis admitted he was ready to rest the Republic of Ireland international for the game, but changed his mind at the last minute.
He said: "I wasn't going to play Jon tonight - I had decided on Friday that I would give him a rest.
"But then after what had happened on Saturday, I decided the best thing to do was to get him out there again.
"And scoring the goals and playing the way he played, I think it's just great for him. It will wash away what happened on Saturday.
"He gives everything, Jon. He is just a very gifted individual in lots of respects, and his biggest asset is his big strong heart and the British bulldog spirit he has got."