The sides were level at 1-1 at half-time, but Viola thumped three unanswered strikes in the second period and Montella felt that this was no more than they deserved.
"The side reacted very well after the break, having struggled under Cagliari's pressure, but the lads proved they really wanted this victory," Sky Sport Italia quotes Montella as saying. "The win was deserved.
"Our ambitions? It all depends on the growth that we see in the team from here to the end of the season."
The win has lifted Fiorentina to fourth in Serie A.