Albert Gudmundsson opened the scoring inside two minutes at the Franchi, with Moise Kean doubling the lead before half-time. Luca Ranieri and Cher Ndour added further goals early in the second half before Davide Lamesta pulled one back for Benevento, sending Fiorentina through to the second round, where they will face the winner of Pisa and Empoli.
Grosso's side also handed debuts to two of the club's newest arrivals. Franco Mastantuono, signed from River Plate, and 16-year-old academy graduate Franco Croci — who became the youngest player to debut for Fiorentina's first team — both came off the bench in the second half.
Speaking to SportMediaset, Grosso praised the pair.
"They both did good things, him and Mazzeo," he said, referring to Croci's cameo. "I tried to put him in a position to show his qualities. We had a bit of a struggle, but he brought a lot of generosity — he has excellent foundations."
Grosso, taking charge of his first official match since arriving at Fiorentina, described a squad still finding its shape.
"We're happy, there's enthusiasm and our ideas are clear. There have been a lot of changes and we've done new things that we need to improve with time. We know that building something good takes a lot of work and a bit of time — we've found a great atmosphere and we'll try to keep it."
Asked whether further attacking width might arrive before the window closes, he left the door open: "Sometimes the system has needed those characteristics. We need to add a bit of quality inside the pitch. We keep changing, but a very difficult league season awaits us and we want to be ready. I'm happy with what I saw, and we'll work to improve — I'll try to put the players who are in the best shape into the ideal conditions for them."
On Mastantuono specifically, who arrived only days before the match, Grosso was full of praise.
"He's very young, but he doesn't seem that young on the pitch in terms of personality and character. He's arrived in the last few days, has very high individual quality and puts himself at the service of the team with a lot of humility. For now we have a lot of potential — we have to bring all of it out and build team unity."