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 City 1 Bolton Wanderers 0: match reportHull, 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.
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 Matthew 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.