Montella's men claimed all three points thanks to a late winner from substitute Marcelo Larrondo.
The Viola coach believes that his side managed to secure an important win thanks to the impact of his second-half changes, which included swapping Stevan Jovetic for Larrondo.
He told Sky Italia: "I went for a player with different characteristics and it worked not only in terms of the goal, but also the pressure.
"It was a tactical change that can happen, even if you are removing a talent like the Montenegrin. We created opportunities and hit the woodwork with Luca Toni, although Chievo made us suffer today.
"We were particularly troubled by their counter-attacks in the first half, but it was clear we were struggling with the tempo. I made some changes and our intensity levels increased. My team looked for the victory with determination and deserved the points. We were more practical than on other occasions."
Fiorentina are now sixth in Serie A, just three points off a Champions League place.