Fuller gave Stoke the lead in an ugly fashion after Robert Huth and Matthew Etherington saw short-range stabs blocked off the line before the Jamaican prodded home.
Jones slotted a second in the final minutes before Lucas Leiva saw red for a second bookable offence to add to Roy Hodgson's woes.
Tony Pulis was forced into making a late change prior to kick-off with the absence of ever-present Abdoulaye Faye handing Andy Wilkinson a start at right-back, while returning centre-back Sotirios Kyrgiakos ousted Martin Kelly in an otherwise unchanged Liverpool line-up from the side that drew at Wigan in midweek.
And it was the Potters who started brightest, pressing their opponents deep in their own half, and saw an early appeal for handball in the box turned down before Ricardo Fuller saw his first chance of the game sail over, moments after Ryan Shawcross had stopped Fernando Torres from screeching down the left channel with a well-timed sliding tackle.
Dean Whitehead, match-winner on Tuesday night against Birmingham City, came close to making it two in two games with a stinging drive that had Pepe Reina at full stretch and came closer minutes later with a sweetly struck half-volley that flew just beyond the Spanish 'keeper's far post.
The reds from Merseyside found it tough going in the early stages, with Stoke pressing high and frustrating the Liverpool midfield, who struggled to find any rhythm, while Reina was not too pleased about some of the Midlands side's blocking on set-pieces, a method by which Kenwyne Jones would come close to opening the scoring when he met a Matthew Etherington corner only to nod it wide.
But Roy Hodgson's team nearly took the lead when Kyrgiakos – who scored what looked like a winning goal when the two side's met in January – rose to meet a corner, only for his effort to be turned away on the post.
It was then the home side's turn to air their grievances to the referee after Lucas Leiva left a late foot in on Etherington in the centre circle, with the winger forced to receive treatment on the sidelines before being able to return to action in a game that was quickly taking a scrappy turn.
But Liverpool edged out the battle and saw two strikes test Asmir Begovic in the Stoke net, first through Steven Gerrard, whose strike was tipped wide by the Bosnian, and then through Raul Meireles, who jinked past two defenders before hitting a left-footed thumper that was well caught by the former Porstmouth man.
Those chances sprung Stoke back into life as Ricardo Fuller deftly controlled a high ball before burning beyond Kyrgiakos and releasing Jones only for the giant striker's first touch to slow down the move, but the club record signing held off Martin Skrtel and delivered a ball across the face of goal that had to be sliced behind by Jamie Carragher as Etherington slid in unopposed at the far post.
After that chance, the game swiftly fell back into its stop-start pattern, with neither team able to consistently hold the ball, but the unusual figure of Wilkinson almost capped a rare league start with an even rarer goal as he cleverly combined with Jermaine Pennant before seeing a wild effort on his weak left foot blocked before it had the chance to cause any danger.
That chance summed up a first half high on energy but low on quality, with neither side creating clear cut chances, but both managers elected to keep personnel as they were for the restart, and Torres' frustration was evidenced when the Spaniard saw yellow for a petulant flick on a downed opponent on the halfway line.
The visitors were becoming increasingly edgy all over, and were fortunate when Reina reacted quickest to a a ropey Konchesky backpass as Jones launched forward, and Hodgson's soon had reason to be glum when Stoke took the lead.
The goal came in typically ugly fashion as Liverpool failed to clear a Pennant cross that saw Robert Huth and then Etherington see goal-bound strikes blocked before Fuller prodded in under Reina.
And the lead was so nearly extended as Kyrgiakos made a mess of a bouncing ball, allowing Jones to slip in unmarked, but the Trinidadian's left-footed half-volley flew wide of the far post.
And Liverpool so nearly punished the Potters as Maxi pounced in a rare Reds move forward, only to be denied from close range by Asmir Begovic.
Hodgson responded to his side's poor performance by throwing on French forward David N'Gog for the disappointing Raul Meireles.
Dutchman Ryan Babel then entered the fray in place of the much maligned Maxi, and the former Ajax man made an almost instant impact, smashing a piledriver from distance that had Begovic stranded, only to see it fire wide.
But Stoke again frustrated their illustrious opponents as Fuller and Jones proved more than a match for Skrtel and Kyrgiakos in the first half, with the latter seeming to stamp on the Trinidadian target man on the halfway line.
And the Potters continued to stymie Liverpool going forward, with N'Gog and Torres frequently forced to go wide and easily mopped up by Wilkinson and Collins.
Substitute Jonathan Walters, who replaced goalscorer Fuller, came close to doubling the advantage with a curling effort from distance as Stoke poured forward on the counter, and the Irishman frustrated fans moments later after dallying on the ball with Jones running through on goal.
But it wasn't to matter as Jones popped up on the stroke of injury time to latch onto a Pennant pass and hold off Skrtel before slotting beyond Reina.
Brazilian midfielder Lucas then saw red for a second yellow card after another late tackle, this time on Etherington, compounding a miserable night for the Reds.