David Pizarro scored the winner for Fiorentina while Mario Gomez hit the post on his debut for the Viola after his move from Bayern Munich, all in the first half.
Rossi, who joined Fiorentina in January, got the game off to an emotional start when he slotted the ball past Mariano Andujar in the 14th minute for his first goal since his injury nightmare.
The 26-year-old's troubles began when he suffered an anterior cruciate ligament injury to his right knee while player for Villarreal in a Spanish league match against Real Madrid in October 2011.
The U.S.-born Italy forward re-injured the knee in training during the following April, causing him to miss Euro 2012, and, after moving to Fiorentina, finally made his comeback against Pescara in May.
Pablo Barrientos, one of nine Argentines in the Catania starting lineup, equalised eight minutes later from close range, rewarding the Sicilians for a spell of pressure.
Chile midfielder David Pizarro rifled Fiorentina back in front from the edge of the area before Gomez hit the post when he should have scored.
Neither goalkeeper had much to do in the second half as the pace of the game dropped.
Twice former champions Fiorentina finished fourth last season, just missing out on a Champions League playoff place, while Catania surpassed expectations by finishing eighth.