Just one place and one point separated the teams before Monday's contest at Stadio Olimpico, but it was the hosts who made the most of Napoli throwing away a two-goal lead in Sunday's 2-2 draw against Inter.
It took just seven minutes for Lazio to make the breakthrough, Lucas Biglia opening the scoring in some style with an excellently controlled volley from the edge of the penalty area.
Lazio continued to swarm the visitors' goal, but found Fiorentina goalkeeper Norberto Neto in fine form - the Brazilian twice making fine stops from stinging Felipe Anderson shots.
Neto was again called into action when Biglia tried to replicate his goal with a similar volley, only for the goalkeeper to tip his shot onto the post this time.
However, there was nothing Neto could to prevent Lazio's second in the 65th minute, Nenad Tomovic's trip on Felipe Anderson led to Antonio Candreva drilling home the resulting penalty.
Klose added the third with a diving header after Candreva's shot was saved by Neto and the World Cup winner tapped home his second five minutes from time to complete the comfortable win.
Stefano Pioli's men subsequently leapfrog Napoli on goal difference to go third, while Fiorentina slip four points adrift of Lazio.
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