Italian striker Di Natale pounced after Palermo keeper Samir Ujkani spilled the ball with seconds remaining.
The goal leaves Palermo - who missed several chances after Thomas Heurtaux was sent off for his second booking in the 61st minute - one point above the relegation zone.
Inter Milan were aiming to move to within a point of league leaders Juventus when they faced Lazio in Rome in Saturday's second game.
Palermo took the lead against Udinese through Josep Ilicic 33 minutes into an even and open first half, when he finished off a swift break by cutting in from the right and hitting a shot that took a freak bounce over the already committed keeper Zeljko Brkic.
Udinese continued to play their part but were poor in front of goal, with Giampiero Pinzi particularly profligate, shooting straight at Ujkani on 53 minutes after being put through.
They looked to have run out of steam by the time Palermo's Egidio Arevalo Rios and Eros Pisano forced two spectacular saves from Brkic on 84 minutes, but Di Natale benefited from Ujkani's embarrassing error.
The keeper looked to have the ball in his grasp but he lost control as he hit the ground, gifting Di Natale the equaliser.
- Sports & Recreation
- Samir Ujkani
- Di Natale