The 29-year-old's double in the additional period at the Britannia Stadium - which put his side 3-1 up - came three days after he had scored a brace of own-goals and missed a penalty in the 4-0 Barclays Premier League loss to Chelsea.
"I wasn't going to play Jon tonight - I had decided on Friday that I would give him a rest," Pulis said of the England-born Republic of Ireland international.
"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."
Extra-time had been forced by npower Championship side Palace thanks to an 87th-minute penalty from substitute Glenn Murray, whose team-mate Jermaine Easter had had a spot-kick saved by Thomas Sorensen in the first half.
Murray's successful strike cancelled out an effort from Kenwyne Jones, introduced from the Potters bench in the 63rd minute and on the scoresheet six minutes later with a header that Palace goalkeeper Lewis Price allowed to slip from his grasp.
After Walters restored Stoke's lead with a 95th-minute header and added a slotted finish with 10 minutes to go, substitute Cameron Jerome wrapped up the victory with the hosts' fourth in the 120th minute.
Palace boss Ian Holloway had praise for Walters as well, but also made it clear he was unhappy his winger Wilfried Zaha, who won the first-half penalty, had been booked for diving moments earlier.
"I think Tony has done a fantastic job," Holloway said. "I think his team are honest, hard-working and never stop, and Jon Walters just sums all that up for me. You see what he did on Saturday, but today you wouldn't have known he ever dreamed of making a mistake. He is a wonderful fella, a brilliant player and a credit to Stoke."
Source: PA
Source: PA