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Udinese had a chance of their own soon after through Bruno Fernandes, who picked the ball up just outside the box and drilled a shot wide of the post.
In the 26th minute the hosts took the lead when Di Natale latched onto a mishit shot at the back post to nod the ball into the net past Gianluca Pegolo.
Udinese were given the chance to score a second 10 minutes later when Diego Farias handled inside the box, but Di Natale blazed the resulting penalty high over the bar.
Sergio Floccari stepped up to take the spot kick, but he placed the ball against the post and could not react quickly enough to score from the rebound.
It proved to be the away side's last chance of the match, as Udinese held on to move 10 points clear of the relegation zone.