Zdenek Zeman's team were rampant in the early stages of the match and were worth an early lead which was manufactured by expansive attacking football.
Erik Lamela got the opening goal when he finished neatly from an acute angle, fooling Zeljko Brkick in the Udinese goal.
The Argentine starlet made in two goals in as many minutes when he headed home an inviting cross from Pablo Daniel Osvaldo.
Udinese slowly recovered from an awful start and were handed a lifeline before half time when Mauricio Domizzi capitalised on some slack defending from the home side to reduce the deficit.
Di Natale kept his nerve from the penalty spot, producing a wonderful Panenka to earn his side all three points and in turn their first away win of the season.
Roma's night when from bad to worse in stoppage time when Panagiotis Tachtsidis was awarded two bookings in a matter of seconds for dissent.