A heavily rotating Inter side dominated the game and opened the scoring after half an hour when Udinese gave the ball away in midfield and Mehdi Taremi's through ball found Marko Arnautovic which finished low into the net.
The hosts doubled their lead just before half-time when Kristjan Asllani scored directly from a corner kick, after a lengthy break due to a medical emergency in the stands.
In the second half, Inter looked to do more damage, and Taremi hit the woodwork with their best chance.
Nine-time Coppa winners Inter host Lazio in the next round in February.
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