The 3-1 home win over high-flying Napoli on Thursday was the perfect way for the defending Serie A champions to begin 2011.
And although Inter fell behind during the second period today when Alejandro Gomez netted for the hosts, Cambiasso quickly turned the match around.
Inter have plenty of ground to make up on leaders AC Milan, after the difficult final weeks of Rafael Benitez's reign, but at least they are starting in a positive manner under new boss Leonardo.
Catania began well, with Maxi Lopez making an early surge into Inter's penalty area before his route to goal was closed off by Ivan Cordoba on the edge of the six-yard box.
Inter had a decent chance in the 13th minute when Maicon crossed from the right and Dejan Stankovic beat defender Pablo Alvarez to the header but saw the ball blocked by goalkeeper Mariano Andujar.
Catania defender Pablo Alvarez had a weak shot from 30 yards comfortably saved by Luca Castellazzi, before Inter rounded off the opening half with Thiago Motta firing over the bar after enterprising play by Stankovic.
Left-back Ciro Capuano went past two defenders before firing over the Inter bar early in the second half, and the visitors were almost punished four minutes later when Christian Chivu failed to make a routine clearance and Pablo Ledesma smashed the ball at goal, with Castellazzi saving well.
Diego Milito drew a save from Andujar in the 55th minute, with a shot to the left corner, but Inter were still seeking the breakthrough.
Maxi Lopez went close for Catania after 68 minutes when Castellazzi had to save with his feet from the striker after a counter-attack.
Catania's goal arrived three minutes later. Stankovic, on the line, cleared a shot from Maxi Lopez only as far as to Gomez, who fired home.
Yet Inter were level after 74 minutes when Stankovic played in Cambiasso and he found the right corner.
And they were in front after 79 minutes when Maicon crossed from the right once more and the midfielder headed into the top right corner.
Inter might have made their victory more comfortable late on, but Milito skimmed the right post in the 89th minute after an assist from Goran Pandev.