After a disappointing opening hour between two of Serie A's most exciting teams, Di Natale broke the deadlock on 79 minutes, cracking his ninth goal of the season after running on to Giampiero Pinzi's fine through ball.
Chilean midfielder Mauricio Isla settled the contest a minute from time, tapping in Pablo Armero's cross to give Udinese their sixth straight home win this season.
"I've rediscovered my team tonight," Francesco Guidolin told Italy's Sky Sport channel, wiping away memories of his team's below-par performance in last weekend's loss at Parma.
"We played according to our strengths and with great courage. We didn't want to give ground to Roma and get punished and that's exactly what we managed."
Whether it was the unusual Friday night kick-off or the 10-minute delay before the start because of a loose net, both Udinese and Roma appeared to lack rhythm in a niggly first half.
With Brazilian centre-half Juan back in coach Luis Enrique's starting XI, Roma employed a high back-line and the first chance for the home side did not arrive until just before the half-hour mark when Moroccan defender Mehdi Benatia headed Di Natale's corner just over the bar at the near post.
Udinese continued to dominate possession and goalkeeper Maarten Stekelenburg was forced into a first save four minutes before half-time, comfortably holding on to Almen Abdi's firm but centrally placed right-foot shot from just outside the box.
The effort appeared to wake Roma up and three minutes after Fernando Gago drove just wide from distance, Miralem Pjanic flashed a left-foot shot wide following a fine move involving Pablo Osvaldo in first-half stoppage-time.
Roma began the second period more in the groove and after Samir Handanovic had turned aside a 30-metre piledriver from Daniele De Rossi, the dangerous Osvaldo shot just over after twisting to find space on the edge of the box on the hour-mark.
Playing on the break, the home side came close to taking the lead four minutes later but after an almighty scramble in the Roma box, Dusan Basta's strike was brilliantly blocked by Stekelenburg.
Di Natale had been kept quiet all night but he finally broke through just as it looked as though the game would end goalless, running on to Pinzi's clipped pass before firing high into the net.
With Roma chasing the game, Isla doubled the home side's advantage at the death, side-footing home from close range after Colombian winger Armero had stolen possession and centred from the left.
Enrique felt Roma did not deserve their fifth loss of the season.
"A draw would have been a fairer result," said the Spaniard, whose side remain fifth.
"Kjaer pulled up for the first goal and then they just hit us on the break. We were a bit more conservative today in going forward as they had five midfielders."
