However, the midfielder's attempt went over the Nerazzurri crossbar.
Cassano sent Rodrigo Palacio through on goal just minutes later with a ball over the Catania defence, but Andujar made a comfortable save from the Argentine's header.
Andujar was called into action on 24 minutes, this time Joel Chukwuma Obi testing him from 25 yards.
Inter eventually broke the deadlock in the 28th minute when Cassano headed home Esteban Cambiasso's delivery from close range.
The second half saw both sides go for the kill in the initial minutes, with Palacio coming close for Inter just before the hour mark.
Inter soon began to take control of the proceedings, with Milito and Ricardo Alvarez testing Andujar.
Andrea Ranocchia was unlucky not to etch his name on the scoresheet in the 77th minute when he saw his header from a Cambiasso delivery come off the post.
However, Inter eventually scored their second goal of the afternoon, Palacio volleying home Milito's pass with just five minutes left on the clock.