The veteran scored the first and set up his side's two other goals as the Giallorossi responded to Napoli's dramatic win over Torino earlier on Monday
The veteran attacker opened the scoring with a precise finish and had a hand in his side's latter two strikes as the Giallorossi held on for three points despite goals from Giampiero Pinzi and Dusan Basta for a spirited visiting outfit.
Captain Totti was welcomed back to the starting XI a month after injuring his thigh, with Daniele De Rossi suspended and both Kevin Strootman and Federico Balzaretti injured.
Udinese, meanwhile, were without the banned Bruno Fernandes and injured Gabriel Silva.
Roma started the encounter brightly and it did not take them long to edge in front. Gervinho found space inside the area and, although his effort was thwarted by Simone Scuffet, Totti was on hand to steer the ball through the crowded penalty area and into the bottom corner.
Udinese pressed to find an instant way back into the match, but just eight minutes later it was 2-0. Gervinho was once again the architect, running into space from Totti's pass and slipping a clever pass into Destro, who poked the ball past the onrushing Scuffet and kept his balance well enough to steer home into the unguarded net.
Morgan De Sanctis denied Antonio Di Natale with a brilliant one-handed stop - a save which prompted the veteran to congratulate the goalkeeper - as Roma ended the half with their two-goal lead intact.
Shortly after the break, however, Udinese grabbed a lifeline. Allan won a free kick from Rodrigo Taddei's foul, and his delivery ended up at the feet of Pinzi, who rifled home a low finish from outside the box.
Di Natale was then denied again by De Sanctis, before Totti fired two efforts narrowly wide as the game opened up.
The veteran would soon play a part in his side's third, however, as he teed up Vasilis Torosidis to drill home from the left of the area.
Udinese responded again, with Allan and Thomas Heurtaux coming close, and with 10 minutes to go they halved the deficit once more, as Dusan Basta fired into the top corner after Roma failed to clear a corner.
The visitors continued to battle for a share of the spoils but ultimately Roma held on to respond to Napoli's earlier win over Torino.