Italy striker Matri arrived on loan from Milan this week to cover injured front pair Giuseppe Rossi and Mario Gomez.
He got off to a great start, flicking the ball to Chile playmaker Matias Fernandez, who opened the scoring with a cool volley on 25 minutes.
Matri quickly added a second with a poacher’s finish from Manuel Pasqual’s low cross, with the ex-Juventus forward completing the scoring four minutes before half-time after Fernandez’s shot was parried by Alberto Frison.
Matri went off at the break after picking up a minor injury, and he late explained how difficult his unsucessful spell at Milan had been.
"I hadn’t experienced a moment like this for a while and to be honest I really needed it," he said.
"I wanted to become a protagonist again and after such a tough time you lose your sense of balance.
"Only my girlfriend and those closest to me know what I’ve gone through."
The result means fourth-placed Fiorentina cemented their chase for a Champions League spot, closing the gap on third-placed Napoli to two points after Rafael Benitez's side were held to a 2-2 draw by Bologna.
Catania stay bottom of Serie A, four points short of safety.