All four goals arrived in the second half with Alejandro Gomez on target twice and Francesco Lodi scoring for the home side, and Luis Muriel netting a consolation for the visitors.
The win lifts the Rosaneri to within two points of the top five heading into the last nine games of the season, giving the Sicilians a realistic hope of taking a place in the Europa League next season.
The first half was practically a non-starter with a very slow pace to a game which dragged on without any drama to the end of 45 minutes.
Udinese forward Muriel tried to provide some inspiration, but he was leading a lone crusade as both goalkeepers left the field at the break without even having got their gloves dirty.
Something had to change in the second half, and it was Catania's Argentinian duo of Gomez and Lucas Castro who brought some much-needed creativity to the match.
They combined to open the scoring in the 49th minute with a neat one-two setting up Gomez to beat Zeljko Brkic with a shot which went in off the inside of the post.
The same combination for the first goal linked up once again in the 67th minute with Castro crossing from the goal line back to Gomez, who headed in from six yards out, wrong-footing Brkic.
Less than five minutes later, Lodi wrapped up victory with one of his trademark free-kicks, his shot from 25 yards dipped in under the crossbar, defying Brkic's attempt to keep the ball out.
Udinese were beaten, but they found a consolation goal with Muriel rewarding himself for an excellent personal performance with a low shot into the bottom corner in the 81st minute.