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The hosts had an early chance to break the deadlock when they were awarded a free kick right on the edge of the Juventus box, but Antonio di Natale's effort flew high over the crossbar.
The opening goal came just over 10 minutes later as Sebastian Giovinco controlled the ball on the edge of the area before drilling a low strike into the bottom corner.
It was 2-0 in the 26th minute as Fernando Llorente reacted quickest to a loose ball inside the area after Udinese had failed to deal with a corner, stabbing it home to double his side's lead.
Udinese could not find a response before half time as the league leaders took a commanding advantage into the break.