The Potters took the lead in the 22nd minute when the visitors squandered possession and Jones made the most of the opportunity, cutting inside and firing home.
It was his first goal since January, and the Trinidad and Tobago striker took only nine minutes to add another, rifling into the net from close range after the ball had dropped at his feet from a corner.
It was all fairly comfortable for the Potters, but Walsall did show some signs of promise in the first half.
And after Charlie Adam had been denied by the leg of Saddlers goalkeeper Richard O’Donnell early in the second period, the visitors got themselves back in the game through Ashley Hemmings’ 57th-minute strike.
Stoke subsequently regained control of the contest, with both Andy Wilkinson and Robert Huth putting the ball in the net but having their efforts ruled out for offside.
And Jones then completed his treble in the 84th minute, racing on to a through-ball and finishing coolly.
It means Potters boss Mark Hughes has a record of two wins from two home games so far since taking charge of Stoke this summer, achieved four days apart.
Prior to that, the last win he had overseen was in August 2012 when he was manager of QPR and they won 3-0, also at home in the second round of the Capital One Cup – against Walsall.
Hughes had vowed in the build-up to this clash to field a “strong” team. The side he ended up selecting featured eight changes from that which had started the Premier League home win over Crystal Palace on Saturday and in the opening stages, the Potters hardly demonstrated their might.
Walsall looked eager to push forward, with Romaine Sawyers in particular appearing a threat, while the hosts were guilty of some sloppy passing.
But the Saddlers struggled for any real penetration while Stoke steadily began to settle down, winning a couple of corners.
And it was then an error at the back by Walsall that led to the opening goal as Sam Mantom inadvertently presented the ball to Jones, who reacted in ruthless fashion with an emphatic finish.
Just after the half-hour mark Jones, scorer of only five goals in the whole of 2012-13, had his second of the evening.
He attempted a header from Jermaine Pennant’s corner and the ball fell nicely for him to slam it past O’Donnell.
Stoke seemed to ease up for the rest of the first half, with mistakes creeping back into their play, but again Walsall were not really able to hurt their opponents.
Hughes made two changes at the break, with new loan signing Oussama Assaidi coming on for his debut along with Marc Wilson in place of Brek Shea and Wilson Palacios.
And looking somewhat reinvigorated, Stoke almost made it 3-0 four minutes after the restart as Ryan Shawcross burst forward and laid the ball square to Adam, whose shot was kept out by O’Donnell’s leg.
Wilson then struck a long-ranger off target but soon afterwards Walsall had the ball in the net, with Hemmings being allowed space in the box to convert from Mantom’s pass.
There was then another defensive lapse as Huth sent an attempted back-pass into Craig Westcarr’s path, but the Walsall striker was closed down by Potters goalkeeper Thomas Sorensen.
Stoke managed to find some momentum again, though, and Shawcross headed wide from Pennant’s corner.
They then had two efforts disallowed for offside, one for Wilkinson and one for Huth, with James Chambers and James Baxendale both blazing over for Walsall in between.
Jones then had the final say, slotting home nicely after being played through by Pennant.