The Reds' six-match unbeaten run came to end as they were outfought, outplayed and outmanoeuvred by Tony Pulis' side.
Fuller opened the scoring just after half-time and Jones completed a comprehensive victory in the final minute before Lucas Leiva was sent off for a second bookable offence.
The Potters were more than worth their win against a team who appear to have lost their way as quickly as they found it.
They have won away from home only once this season and only three times since last November.
Their first 45 minutes appeared to be a direct continuation of the second half at Wigan, where they had found themselves under almost constant pressure and were lucky to come away with a draw.
Only the returning Sotirios Kyrgiakos had not played in the previous two matches so there may have been an element of fatigue, especially as Stoke played a day earlier on Tuesday.
But no team in the Premier League, let alone a club like Liverpool, can expect to use that as an excuse for an abject and disjointed first-half display.
Roy Hodgson's side appeared unprepared and unable to deal with their hosts' brash, energetic approach which allowed them to dominate the game from first to last.
Stoke were appealing unsuccessfully for a penalty in only the second minute when Maxi Rodriguez leant heavily on Ricardo Fuller as they challenged for Rory Delap's long throw.
It was a sign of things to come as the visitors found themselves being forced back, looking worrying susceptible to Delap's trademark set-piece.
Midfielder Dean Whitehead benefited from weak headed clearances to fire in a low shot which Jose Reina turned around a post and then drill a similar 30-yard effort just past the angle of upright and crossbar.
Jones and former Reds winger Jermaine Pennant also had chances before Steven Gerrard registered Liverpool's first shot in the 29th minute, forcing Asmir Begovic to tip the low effort behind, although the goalkeeper dealt more comfortably with Raul Meireles strike from the resulting corner.
It was a brief retort which was soon forgotten when Jones rounded Paul Konchesky to cross low into the six-yard box, forcing Jamie Carragher to dive in front of Matthew Etherington to prevent the opening goal.
Less than two minutes into the second half Fernando Torres, who had been anonymous previously, was booked for tackling Pennant from behind.
But the real threat was still coming from Delap and Liverpool's inability to cope with his party trick finally cost them in the 56th minute.
A scramble saw the ball break to Etherington at the far post and his cross-shot bounced back off Konchesky to Fuller, whose had his first effort blocked but stabbed home the second from close range.
Despite the stereotype, it was Stoke's first goal from a Delap party-piece in 23 league matches.
Jones almost made it two when Martin Skrtel mistimed his jump but his left-footed effort beat both Reina and the far post.
Liverpool, as they did in the first half, had two chances in quick succession with Rodriguez shooting straight at Begovic from Dirk Kuyt's cut-back and Skrtel firing wide from Kyrgiakos' knockdown of Gerrard's free-kick.
David Ngog and Ryan Babel replaced Meireles and Rodriguez but with Liverpool still unable to gain decent possession of the ball it made little difference they effectively had four strikers on the pitch.
Their embarrassment was completed in the 90th minute when Gerrard gave the ball away and Jones was able to skip past Skrtel to fire home.
The dismissal of Lucas just compounded matters.
In terms of territory and control Liverpool have now lost the last five halves they have played in.
The 45 minutes prior to that had been the electrifying first-half display against Chelsea but team now appear to be on a downward spiral again.
It is a descent Hodgson has to arrest quickly. He left the Britannia Stadium with chants of "Dalglish" - a reference to former player and manager Kenny - ringing in his ears.