The boss chose to shuffle his pack with the Bianconeri's upcoming midweek exploits in the Champions League in mind and they fell behind to a Jakub Jankto strike.
However, a brace from Paulo Dybala saw them secure a fifth straight win in all competitions, in the process restoring their five-point lead at the top of the table following Roma's win at Napoli earlier in the day.
Allegri admitted after the match that things were not easy for his side on Saturday but says carving out scrappy wins like this one will be the key to them claiming a sixth straight Serie A title.
"It was a very complicated match, which we made even more complicated, because we should've taken chances better," he told Sky Sport Italia.
"We lost a player every day, including two this morning, but Scudetti are won via games like this and we approached it the right way."