Serie A's second-bottom club headed into the encounter at the Stadio Adriatico-Giovanni Cornacchia in awful form after losing six of their last seven matches and sadly for them, that poor form continued.
Pescara remain five points clear of safety but a win for Genoa at Roma later this evening will see Cristiano Bergodi's side way off the pace.
The home side could have taken the lead inside the opening minute, but Elvis Abbruscato headed over Manuel Blasi's right wing cross.
The visitors took full advantage of that missed opportunity seven minutes later when Luis Muriel's cross from the right was converted by Di Natale from close range.
Zeljko Brkic pulled off a decent save in the 12th minute to keep out Emmanuel Cascione's long-range free-kick, while Luciano Zauri missed the target 10 minutes later from distance.
Muriel was causing havoc down the Udinese right and once again he crossed for Abbruscato - but once again he could not find the target.
Two minutes before the break Udinese could have been two ahead but Ivan Pelizzoli did well to keep out Thomas Heurtaux's shot.
Vladimir Weiss was denied by Brkic two minutes into the second period before Muriel's effort from distance flew over Pelizzoli's bar.
After 65 minutes Cascione failed to find the target from distance as Pescara found chances hard to come by.
Gianluca Caprari was the next home player to fail to test Brkic as time ran out for the home side.
In truth Udinese went closest to scoring the closing stages after Loureiro Allan beat two players before firing an effort on goal which ended up just wide of the post.