Antonio Di Natale's third goal in his last four games unlocked the game for the Friulian side.
Bruno Fernandes and Emmanuel Badu completed the rout to take Udinese nine points clear of the drop zone.
The win also means Udinese can go into their midweek Coppa Italia decider with Fiorentina in confident mood.
Buoyed by a 2-1 win over Fiorentina in the first-leg of that semi-final tie on Tuesday night, Udinese were looking to transform their cup form into league points to lift them away from the danger zone.
It looked like they were in cup mode too when Andrea Lazzarri fired a shot just wide early on, but Chievo resisted their early attacks.
The visitors almost snatched the lead on the half-hour mark when Cyril Thereau hit the post with a backheeled effort at the end of a swift counter-attacking move.
Chievo continued to sit back, soak up the pressure and seek chances on the break, but they almost came undone 10 minutes before half-time when Lazzari teed up Antonio Di Natale, but his delicate attempt to lob Christian Puggioni saw him simply hand the ball to the Chievo custodian.
There was nothing at all simple about the execution of a volley which gave Udinese the lead in the 56th minute as Di Natale latched on to Dusan Basta's ball to continue his recent scoring spree.
He then put Pereyra through to square low for Fernandes to make it two in the 76th minute and effectively put the points in the bank for the Zebrette.
Di Natale was subsequently removed with coach Francesco Guidolin already starting to think ahead to Wednesday's Coppa Italia semi-final second-leg trip to Fiorentina, a game they will now go into with even more confidence after Badu completed the comfortable victory over Chievo.
Luis Muriel and Bruno Fernandes were both involved in setting up the winger, who side-footed the ball in to secure the points.