The Roman side had the game's first chance and it came in the fourth minute when Antonio Candreva shot at the Viola goal from outside the box but failed to keep it on target.
Minutes later Bizarri was called into action by a Manuel Pasqual effort from outside his penalty area.
The hosts were then gifted a great chance to take the lead at Stadio Artemio Franchi, when Abdoulay Konko conceded a penalty by bringing down Pasqual inside the Lazio box.
However, Matias Fernandez failed to convert the spot kick, shooting against the post.
Fiorentina, though, did break the deadlock and the goal came on the stroke of half-time, Adem Ljajic firing in from outside the area.
Ljajic almost doubled the Florence outfit's advantage at the start of the second half, but his shot was saved by Bizarri.
Klose himself tried his luck with a close-range shot but could not keep it on target.
Three minutes later things went from bad to worse for Lazio, as they went to reduced to 10 men after Cristian Ledesma was sent off for a second bookable offence.
Lazio finished the game with just nine men on the pitch, as playmaker Hernanes was dismissed with just eight minutes left on the clock for a rash challenge.
The two-man advantage helped Fiorentina score their second goal of the afternoon in the final minute of normal time, as Toni shot home Alberto Aquilani's cross from close range.