Walters scored either side of Kenwyne Jones' header after the visitors had taken the lead through a Steven Gerrard penalty awarded in the first minute.
The Merseyside-born 29-year-old was the match-winner on this ground in September 2011 with the only goal from the spot.
There were 32 seconds on the clock when Luis Suarez broke into the right-hand side of the penalty area and was pulled back by Ryan Shawcross and referee Howard Webb immediately pointed to the spot.
It was the first time in 32 matches Liverpool had been awarded a penalty and Gerrard was in no mood to squander the opportunity as he coolly stroked home for the third successive league game - a feat last achieved in December 2007.
However, the celebrations were short lived as the home side were not only level four minutes later but ahead with just over 12 minutes gone.
A customary long ball forward could only be flicked backwards by Daniel Agger and with Martin Skrtel losing his footing Walters capitalised to smash a shot past Jose Reina.
The aerial bombardment continued but there will be questions asked in the Liverpool defence about Stoke's second from a corner as Jones was able to jump virtually unchallenged to head in at the undefended near post.
Liverpool's hopes of getting back on level terms quickly were extinguished with Walters' second of the night after 49 minutes.
The defence again failed to deal with a long throw as Jones flicked on for his strike partner to control the ball on his chest and hammer home a dipping volley.
- Sports & Recreation
- Kenwyne Jones