After Luis Suarez won a first-minute penalty that Steven Gerrard converted, a Walters brace and a rare goal for Jones extended the Potters’ unbeaten league run to nine matches, with Jones headers creating both goals for Everton fan Walters.
The result puts Stoke above Liverpool into eighth, with the Reds three points behind.
Gerrard made no mistake from the spot, sending Asmir Begovic the wrong way and the ball into the bottom left, with the home fans’ anti-Suarez chants ludicrous given the obvious nature of the foul.
But Liverpool’s lead was cancelled out in two minutes after Martin Skrtel, whose brilliant long ball sent Suarez through for the penalty, slipped at an inopportune moment to allow Walters to meet Jones’s flick-on to finish past Pepe Reina.
The much-maligned Jones, preferred to Peter Crouch after the former Liverpool striker’s loss of form, turned from provider to scorer when he headed in a rare goal from a Glenn Whelan corner, although the marking of Gerrard and goal-line efforts of Glen Johnson left something to be desired.
Within 10 minutes Stoke had turned things round, but Liverpool responded with an intense spell of pressure for the remainder of the half.
But the Reds failed to level before the break, thanks in part to some poor finishing from Suarez, while Gerrard put a couple of efforts wide.
Indeed, Stoke could have extended their lead but for an excellent stop by Reina, who smothered Matthew Etherington’s finish after he had been found unmarked in the box.
Rodgers made the expected half-time change by introducing Raheem Sterling for Suso, and the England winger almost had an immediate impact as his clever run down the left should have seen Suarez level – but the Uruguayan put wide with just Begovic to beat.
And Stoke made them pay with Jones once more combining with Walters, this time the Trinidad and Tobago striker flicking the ball across goal for the Ireland forward to control on the chest before planting a sweet finish past Reina.
A two-goal cushion is some advantage at the Britannia but the hosts wanted more as they sought to get Jones on the ball as often as possible, the home fans ironically singing rugby songs in tribute to their physical style.
Despite an absence of obvious chances for an extended spell, the match was still enthralling enough as both sides traded attacks for fun.
Liverpool were let down by their final ball, but their defenders were relatively alert as Walters and Jones continued to dovetail impressively.
Stoke have a strong squad these days and Tony Pulis replaced Jones with Crouch, the former England striker having stated the season well but tailed off in recent weeks.
There were some half-chances for the visitors late on, but Suarez wasted a free-kick before playing a fantastic ball across the face of goal that none of his team-mates showed for.
That was the end of their hopes of a comeback as Stoke closed out a great win to extend their fantastic run, which has also seen them unbeaten in 16 home matches.
MAN OF THE MATCH
Jon Walters (Stoke): The Everton fan's brace included a majestic touch and finish that will be lost on the world simply because it was Stoke.
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