The Premier League side ran out comfortable winners over their lower-league opponents, with the Republic of Ireland international in inspired form at the Britannia Stadium
Making his first appearance of the season, the Republic of Ireland international staked a claim for a starting spot for the trip to Manchester City in the Premier League on Saturday.
Stoke have garnered just a point from their opening two league fixtures this season, but this win at the Britannia Stadium will come as a welcome boost ahead of the daunting trip to the champions at the weekend.
Walters claimed his first goal shortly after the quarter-hour with a close-range finish, before he was well set up by debutant Victor Moses at the start of the second half to double his tally.
Stoke dominated proceedings throughout - visiting goalkeeper Paul Jones making a number of fine saves to keep the scoreline down - although he was beaten again when former Portsmouth man Peter Couch added a third with a trademark header in the final minute.
For Portsmouth, it was a first competitive defeat under Andy Awford, who had previously guided the team to a 12-match unbeaten run since taking over in March.
Mark Hughes made nine changes from the side that started Sunday's 1-1 draw at Hull City, including a first appearance for Robert Huth since suffering a knee injury in November.
Portsmouth made eight alterations from their 1-0 win at Oxford United, with Awford handing a first-team debut to son Nick.
Following a quiet start, Stoke went ahead in the 16th minute as Walters nipped in front of Jones and prodded Marc Muniesa's cross into the net.
Jones had to be alert to prevent the visitors from falling further behind two minutes later, producing a fine double stop to keep out Moses and then the rebound from Crouch.
Moses continued to threaten, setting up Walters for a header that was saved, before Crouch volleyed narrowly over the crossbar.
Portsmouth were struggling to get to grips with Moses, who then saw a powerful shot deflected narrowly wide after another surging run in the 32nd minute.
Jones performed more heroics on the stroke of the interval by somehow keeping out Huth's close-range effort as the visitors were grateful for the half-time whistle.
Walters doubled his tally just two minutes after the restart, though, converting at the back post after Moses had got free down the left and sent a low delivery across the six-yard box.
Though a sprawling Jones denied Walters a hat-trick, he could do nothing to keep Crouch's late header out as Stoke added some gloss to the result.