- Nicolás González (3')
- Lautaro Martínez (29', 37')
With both teams preparing for major European finals next month and meeting for the first time in a major domestic final, Inter made nine changes from Sunday's defeat by Napoli, starting in-form striker Romelu Lukaku on the bench and Samir Handanovic replacing Andre Onana in goal.
"We started badly and had the wrong approach, which is rare for us, but the lads did well to stay in the game anyway and then turn it around," Inter manager Simone Inzaghi told Mediaset.
"I am happy, because we won a cup that we wanted, to confirm what we did last season. Fiorentina are a quality team who caused us a lot of problems."
Inter have had a successful season, retaining the Coppa Italia and Italian Supercup titles and reaching next month's Champions League final against Manchester City.
"We have the final two Serie A games, then Istanbul and a great season we want to keep going," Inzaghi added.
Argentine Martinez did level with a shot from a tight angle in the 29th minute and followed up with a close-range volley high into the net eight minutes later.
Martinez now has a career-best 27 goals across all competitions for Inter this season, having also helped Argentina win the World Cup in December. He's also the only player to have appeared in all 54 of Inter's matches this season.
"In all honesty, I am moved, because for a few years, we have been bringing trophies to this great club, and we must continue like this. I am very happy," Martinez said.
"I am very happy to bring this trophy back to Milan, or rather keep it there, seeing as that's where it was last year."
Fiorentina rarely threatened to get back into the match and Terracciano showcased his goalkeeping skills by making a remarkable double save to deny Lukaku's powerful strike and Federico Dimarco's follow-up.
Fiorentina's best chance to equalise came when Luka Jovic's strike was saved by Handanovic but Inter held out comfortably before celebrating their ninth Coppa Italia title. Inter coach Simone Inzaghi has now won seven of his eight finals as a manager.
Fiorentina face West Ham United in the Conference League final on June 7 and Inter play City in the Champions League final on June 10.
"We were hoping for a different result but this will serve as experience and preparation for what to expect on a mental level and how to handle the match for the Conference League final," Fiorentina coach Vincenzo Italiano said.
Information from the Associated Press was used in this report.
- Massimiliano Irrati