Just two weeks after going down 3-0 at home to Napoli, Claudio Ranieri's side lost again, despite taking a sixth-minute lead through Esteban Cambiasso.
Sergio Almiron and a Francesco Lodi penalty turned the game around in the second half, as the Sicilians took a deserved three points to leave the Nerazzurri five points behind them in the table after six games of the season.
Catania made their intentions clear from the outset with some quick attacking football, but it was Inter who went ahead with their first chance of the game in the sixth minute.
Maicon's long cross from the right was met on the volley by Cambiasso, whose shot arrowed into the far corner of Mariano Andujar's goal.
The home side continued to dominate, although Inter goalkeeper Luca Castellazzi was never threatened in the first half.
He had to pick the ball out of his goal just two minutes into the second half, though, when Almiron curled a first-time shot into the top corner after receiving the ball from Gonzalo Bergessio to finish off a textbook counter-attack.
Two minutes later, Bergessio raced through and touched the ball past Castellazzi before falling over the Inter goalkeeper's arm.
The referee Daniele Orsato was fooled and pointed to the spot, showing Castellazzi a yellow card.
Catania's set-piece specialist Lodi stepped up to put Catania in front.
Inter tried to attack, but the best chances fell to Catania on the break with Gennaro Delvecchio denied by the legs of Castellazzi in the 75th minute and the Catellani failing to beat the Inter goalkeeper in another one-on-one situation in the 82nd minute.
Catania then resisted Inter's late assault at the Stadio Massimino.