The Argentina international – who entered the match with three goals from two matches this season – produced a superb performance as Inter maintained their 100 per cent record under new manager Walter Mazzarri.
Palacio opened the scoring for Inter in the 19th minute before he turned provider after the break, setting up Yuto Nagatomo.
And Ricky Alvarez sealed the result 11 minutes from time with a sensational effort, as he raced through the Catania defence before producing a stylish left-foot finish.
Mazzarri has overhauled the Inter squad in the transfer window, bringing in a host of players as the San Siro outfit aim to improve on last season's ninth-place finish.
And the former Napoli boss already looks to be having an impact, as the Italian giants were excellent in Sicily.
Inter made just one change to the side that beat Genoa 2-0 last week as Mateo Kovacic replaced Zdravko Kuzmanovic in the midfield.
Catania coach Rolando Maran also tinkered with his squad, selecting Nicola Legrottaglie and Sergio Almiron in place of Giuseppe Bellusci and Pablo Barrientos.
Both sides traded superb chances in what was a frenetic start to the match, with Sebastian Leto shooting straight at Inter goalkeeper Samir Handanovic with the goal gaping.
Inter immediately countered and Legrottaglie was forced to clear off the line after goalkeeper Mariano Andujar failed to handle Jonathan's fierce drive.
Mazzari's men soon set about exerting their dominance and they claimed the lead in the 19th minute as Palacio tapped in from close range.
Jonathan created the goal, breaking free down the right before delivering a superb low cross into the path of the in-form Argentinian.
Inter soon sat back after taking the lead, though, allowing their opponents into the contest, and Panagiotis Tachtsidis and Almiron went close with efforts on goal before the break.
Nagatomo went close early in the second half, with his far-post header brilliant saved by Andujar, but Inter got their second goal 10 minutes after play resumed.
Palacio did well to get free on the right before delivering a superb cross which Nagatomo finished with aplomb.
Alexis Rolin forced a good save out of Handanovic at the other end, while Inter were initially denied a third goal when substitute Ishak Belfodil was adjudged offside after finishing from close range.
They did score again though, as Alvarez picked the ball up just inside the Catania half, before weaving past several defenders and firing past Andujar.
The upcoming international break will give Mazzarri two weeks to prepare for a crucial home fixture against Juventus, while Catania's next assignment is at Livorno.
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