The Belgian striker, signed from AZ Almaar last month, equalised after half-time and then hit an 89th-minute winner shortly after Wolves defender Christophe Berra was sent off.
Liverpool?s next 10 games to get title bid back on trackDembele's powerful performance in attack helped soften the blow for Fulham, who lost striker Bobby Zamora with a serious ankle injury in the first half.
The result ended Wolves's unbeaten record in what had been their best start to a Premier League season, but they have won few friends because of their physical approach and had Fulham's fans chanting: "Disgrace to the Premiership" at Mick McCarthy's men.
The Wolves manager must also deal with a fine after his team incurred seven yellow cards, including the dismissal of Berra for a second caution. From the resulting free-kick, justice appeared to be done as Simon Davies and Zoltan Gera teed up Dembele to fire a shot through the wall from 25 yards and complete a deserved victory.
Wolves had opened the scoring in controversial style in the tenth minute when Jelle Van Damme - another Belgian - scored his first goal since being signed from Anderlecht in the summer.
Fulham's players and supporters felt that Kevin Doyle fouled Brede Hangeland in the build-up play, but even so the Irishman's cross should have been intercepted by John Pantsil in front of his own goal before the ball sailed through for Van Damme to hit home on the half volley at the far post.
Fulham already felt aggrieved that they had not been given a penalty by Phil Dowd five minutes earlier when Davies appeared to be tripped in the area by Berra after a neat exchange of passes with Dickson Etuhu. It was one of three unsuccessful appeals by Davies.
Fulham were awarded a free-kick in a dangerous position shortly afterwards when Karl Henry fouled Fulham's new signing Dembele, but Zamora struck his shot high over the bar from 20 yards.
The Fulham striker tthen suffered a cruel blow in the 28th minute when he went down in pain after a challenge from Karl Henry and had to be taken off on a stretcher with what looked like a serious ankle injury.
But Dembele equalised early in the second half and the game really came to life. The ball was only half-cleared after a cross from the left and Dembele was on hand to control it with his right foot and shoot home with his left foot from 15 yards.
Both sides could have scored more after that. Gera went close with an overhead kick and Davies flicked a good chance just wide, while Wolves also had chances when Doyle's header was brilliantly saved by Mark Schwarzer, back in Fulham's goal.
But it was Dembele who had the last word with the wnning goal, and a first win of the season for Mark Hughes after three successive draws.