Leeds looked locked on course for a vital point when Ian Moore cancelled out Mamady Sidibe's opener, before an Ugo Ehiogu own goal turned the tide against the visitors.
Fuller netted his sixth of the season with an alarming amount of ease to condemn United to the third defeat on the bounce away from Elland Road and more ominously their eighth in Dennis Wise's 13-game tenure.
Wise deployed a new-look line-up following Boxing Day's two-goal reverse at the hands of Sunderland in the hope of containing the Potters' attacking threat.
David Healy, Ian Moore and Jonathan Howson were all promoted from the bench into the boss' cautious 4-5-1 formation, but after only 12 minutes frailties were exposed.
Some crafty approach play twice got Fuller past United's security only for the linesman's flag to thwart the striker's attempts at a conversion.
The hosts did eventually find their timing and got a deserved reward for an all-action opening 12 minutes - Sidibe claiming his third of the season.
The towering frontman rose above any challenge to nod home Lee Hendrie's floated flag-kick for his second goal in a bumper five days at the Britannia.
Leeds have only managed one clean sheet in a dismal season on the road and after the opening 15 minutes the reasons behind their poor away record were no mystery.
But as the visitors shook their defensive nerves, Wise's five-man midfield began to make real in-roads into an increasingly casual home side.
Healy and Jonathon Douglas both wasted good chances to restore parity before Moore struck with only four minutes remaining in the first half.
The forward powered in his first goal since October after getting on to Healy's pin-point centre to draw his side level - a scoreline which flattered Stoke more than the struggling visitors.
Crowd favourite Hendrie concluded his three-month loan spell with the Potters by making way for fellow Villa loanee Patrik Berger at the break.
And no sooner was the midfielder back down the M6 than the Britannia faithful were celebrating his replacement's introduction.
Berger took aim from the edge of the box and slammed back an idly cleared corner which ricocheted fortuitously off the hapless Ehiogu and past the rooted Tony Warner.
Fuller finished the visitors off when he pounced on a mix-up between Warner and Ehiogu in the 77th minute to stroke his sixth goal of the season into an abandoned net.
Sidibe and Berger had opportunities to apply the gloss to a faultless second-half showing from the Potters, but interventions from Ehiogu and Warner respectively kept the deficit to a minimum.