Jamaica international Fuller, whose brilliant individual effort beat West Ham last week, capitalised on a sixth-minute error by defender Paul McShane to clip a shot past Boaz Myhill.
Hull, who played the last 15 minutes with 10 men after captain George Boateng was knocked unconscious by a Tuncay Sanli overhead kick, deserved more for a spirited second-half performance but conceded late on.
The result ended a run of four matches without a win at the Britannia Stadium and lifted the Potters up to 10th but left Hull still mired in trouble near the foot of the table.
It also extended the Tigers' record to one win in their last 30 Premier League away matches, having not tasted victory on an opponent's ground since Fulham on March 4 last year.
It was not difficult to see why that record was so woeful as they went behind after just six minutes.
Centre-back McShane completely misjudged Dave Kitson's flick-on and allowed the ball to get behind him.
It was a calamitous error as Fuller raced past the defender and clipped a shot with the outside of his right foot past Myhill.
McShane's desperate recovery tackle only succeeded in injuring the Potters striker, who despite scoring in successive games only has three Barclays Premier League goals this season, but he limped back into the action after treatment.
Robert Huth volleyed over from Rory Delap's long throw for only the second decent chance created by either side in the opening 25 minutes.
McShane, who was struggling to contain the lively Fuller, also had to dive in to block Kitson's near-post deflection as Stoke cranked up the pressure.
Craig Fagan was lucky to avoid a booking - or worse - after kicking out at Matt Etherington in the 42nd minute as Hull continued to struggle to gain a foothold in the game.
The non-appearance of the injured Fuller for the second half, however, had a debilitating effect on Stoke as his replacement, Sanli, could not produce the same energy or threat.
They had a let off when Fagan's first touch was so bad he knocked the ball out of play just when it seemed he had got clear in the six-yard area.
At the other end Kitson just failed to get his head to Lawrence's right-wing cross but it was Hull who were looking the more dangerous.
Abdoulaye Faye's foul on Richard Garcia, pulling back the midfielder after he had gone past him, earned him a yellow card but Jimmy Bullard drilled the 20-yard free-kick into the wall.
The introduction of Geovanni for the ineffectual Dean Marney just before the hour reflected Hull's need to take advantage of their best spell of the match.
But the Brazilian failed to live up to his reputation for spectacular strikes when his first attempt at goal from outside the penalty area bobbled embarrassingly wide.
Bernard Mendy was cautioned for hauling back Etherington and Danny Higginbotham's flicked header from the winger's set-piece went over the crossbar.
But Hull continued to dominate and from Geovanni's cut-back on the left of the penalty area, Fagan saw his shot charged down by Higginbotham and Boateng's rebound blocked by Glenn Whelan.
Stoke's opportunities were becoming increasingly fleeting but Kitson was denied twice in the space of a few seconds from Rory Delap's long throw.
There was a lengthy delay for Boateng's injury as the Hull capin was carried off on a stretcher to a waiting ambulance.
With boss Iain Dowie having earlier sent on Jozy Altidore and Jan Vennegoor of Hesselink for Garcia and Folan it left Hull a man short.
Tuncay should have made the game safe for Stoke with seven minutes to go when Myhill's scuffed clearance reached him 25 yards out but he screwed badly wide of an empty goal.
But Lawrence made no mistake in the 90th minute when put through by Etherington, sliding a shot across Myhill and into the far corner of the net.
Eight minutes of injury time followed but the fight had been knocked out of Hull, who will feel a sense of injustice that they did not get what they deserved.