The Potters allowed the Reds to take a second-minute lead when Steven Gerrard converted form the penalty spot but struck back when Walters netted just three minutes later.
Kenwyne Jones made it 2-1 to the home side in the 12th minute before Walters grabbed his second four minutes into the second half as Stoke moved up to eighth on the table and the performance was well-received by the match winner.
"We all work for each other, right from the back to the front. It was a full team effort from us today and a great win for us," he told Sky Sports 1.
"We haven't conceded many this year, and to concede so early...but we've always got fight in us, and there was never any chance we were just going to lie down and take it.
"So from 1-0 down we showed great character to get back into the game and some good play from all over the team, especially the second half."