The Giallorossi had trailed but the Belgian equalised on the stroke of half-time before the 29-year-old sealed three vital points after the break
After a sedate opening, Stipe Perica gave the visitors the lead, striking home from close range before Radja Nainggolan drew Rudi Garcia's side level on the stroke of half-time and Vasilis Torosidis proved to be an unlikely hero with a winner after the break.
Roma needed to win to leapfrog city rivals Lazio, who led them by just two points in the table at the start of play. However, after an opening 20 minutes which saw both sides probe, it was the visitors who took the lead.
After some dozy defending from Kostas Manolas, Cyril Thereau ran into the box from the left wing and forced a save from Morgan De Sanctis, but he could only bundle the ball into the path of Perica, who gleefully smashed the loose ball home.
Falling behind sparked the hosts into life. Francesco Totti had already forced a fine save from Orestis Karzenis with a powerful free kick when the veteran captain brilliantly picked out Nainggolan at the far post and the Belgian had plenty of time to pick his spot and level proceedings.
Though time was rapidly running out before the break, Udinese were a whisker away from restoring their lead when Mapou Yanga-Mbiwa gave away a free kick in a promising position. Guilherme stepped up and slammed his effort off the top of the crossbar and over.
The second half started with the defences on top once more as both sides probed for an opening but to no avail. Ironically, it was an error at the back which allowed the hosts to complete the turnaround.
Udinese failed to clear their lines after a Roma attack, with Silvan Widmer slicing a clearance, allowing Torosidis to pounce and scramble the ball home.
After taking the lead, Roma were the dominant force in the clash but failed to kill off the visitors, twice striking the woodwork late on, firstly through Nainggolan's back-heeled effort and secondly through Jose Holebas, who strode into the box and smashed a shot off the bar.
However, the misses did not prove costly and Roma moved second by a solitary point with two games left to play. Udinese, meanwhile, remain comfortable in mid-table.