The striker bagged two goals at the right end in extra-time following his two own goals and a missed penalty in their Premier League hammering against Chelsea at the weekend.
Kenwyne Jones handed the Potters the lead midway through the second half, but Palace, who had earlier missed a penalty, were handed a second opportunity which Glenn Murray duly dispatched to send the third round replay into an extra 30 minutes.
Walters struck his first with a fine header before adding a second to secure victory early in the second period.
Cameron Jerome added the icing on the cake for Tony Pulis' side with a strike in the dying moments.
The match started well for the side from south London as they were handed a wonderful opportunity to open the scoring 11 minutes before the interval when referee Anthony Taylor pointed to the spot.
Ryan Shawcross brought down the tricky Wilfried Zaha in the area, however, goalkeeper Thomas Sorensen made a flying save to deny Jermaine Easter.
Substitute Jones then made an immediate impact soon after replacing Peter Crouch midway through the second half.
The striker curled a lovely effort from the edge of the area which struck the post, but then he did break the deadlock after 69 minutes. Matthew Etherington's cross was met by the Trinidadian, but goalkeeper Lewis Price held his hands on his head after failing to deal with a routine catch.
The Championship outfit deservedly restored parity after they were then handed a second opportunity from the penalty spot with just three minutes of the 90 remaining.
Jonathan Williams was hacked to the ground by Shawcross and the club's usual penalty taker Murray - who had just come on - stayed calm, cool and composed to power the ball high into the top corner past Sorensen.
The game - which followed a 0-0 draw at Selhurst Park 10 days ago - went into extra-time and within five minutes of the opening period, City went ahead as Etherington's cross was powerfully headed into the back of the net by Walters who made amends following his miserable weekend.
And he was soon at it again, slotting the ball home from close range after being set up by Jones. And City made it four deep in stoppage time thanks to Jerome's cool finish after fine work once again by Jones.
Stoke now face a home clash with Manchester City, a fixture that will bring together the two teams that contested the 2011 final.