The Nerazzurri finished a dismal ninth last season but, under the supervision of former Napoli boss Mazzarri, claimed a regulation victory over Genoa on the opening day of the new campaign.
Rodrigo Palacio and Yuto Nagatomo, who both scored last weekend, were on target again at the Stadio Angelo Massimino while Ricky Alvarez cemented a result which would have been off limits to the Inter side of six months ago.
Catania were first to threaten, Lucas Castro trying his luck from distance, but Inter goalkeeper Samir Handanovic made a comfortable save.
Gonzalo Bergessio came knocking in the eighth minute but once again Handanovic was wise to the move and parried, allowing the visitors to break.
Jonathan soon found himself in a good position on the right side of the box at the end of the move but Mariano Andujar denied the Brazilian.
Alvarez pinged the ball wide from a Fredy Guarin cross but in the 19th minute Inter would make the breakthrough their creativity deserved.
More good movement from Jonathan saw Palacio released in the box and the Argentinian tucked home from close range.
Catania battened down the hatches and, on 31 minutes, Panagiotis Tachtsidis even came close to equalising with a fearsome strike from range.
Sergio Almiron tried to repeat the trick before the break but his drive took a deflection and veered just wide.
That was a clear warning for Inter who responded in the perfect way when play resumed.
Moments after the restart Nagatomo had Andujar sprawling to save his bullet header but in the 49th minute the Catania keeper was beaten by the Japanese winger.
This time Palacio turned provider with a soaring cross from the right wing that Nagatomo tucked away at the far post.
Catania were fighting an uphill battle to wrest control of the match from that point forward and, after Alexis Rolin had been denied by Handanovic, Inter made it 3-0.
It was easy for the Nerazzurri this time, and Alvarez was unopposed as he skipped through the home defence to beat Andujar with a cool left-footed finish via the far post.
Substitute Ishak Belfodil might have added insult to injury with a fourth goal on the stroke of full-time, but he could not get the connection he needed when sliding in to reach a loose ball in the Catania box.