Neither side gave the other an inch during a goalless first half, but the visitors came close in the 20th minute when Alexander Merkel shot narrowly wide from the edge of the box.
Udinese had significantly more attempts on goal in the first period, but it wasn't all one-way traffic. Visiting goalkeeper Alberto Frison denied both Gomez and Lucas Castro to keep the score at 0-0 going into the break.
Catania stole the lead early in the second period when Gomez rifled home from inside the box after being lined up by Castro.
The hosts extended their advantage in the 67th minute. Pablo Barrientos supplied the cross and Gomez was on hand to punish Udinese again, heading beyond Frison to make it 2-0.
Catania's third came directly from a free kick in the 71st minute, which Francesco Lodi belted home to put the game beyond their opponents.
Udinese did pull a goal back through Luis Muriel with less than 10 minutes left on the clock, but it proved to be no more than a consolation.