Having dominated large parts of the opening exchanges, travelling Udinese broke the deadlock with 17 minutes played. Di Natale was the provider, crossing for an unmarked Danilo to head into the net from close range.
Udinese went on to double their advantage 11 minutes later. Gaetano Berardi scuffed his clearance and Di Natale took full advantage by rolling the ball into an empty net.
Hosting Samp had a greater attacking threat after the restart and managed to win a penalty just after the 60-minute mark. However, Nicola Pozzi's effort from 12 yards out was saved by Zeljko Brkic in goal.
Di Natale had further chances to extend Udinese's lead in the closing stages, but he was unable to add to his and his side's tally.
The win has lifted Udinese up to eighth in the Serie A table.