Cyril Thereau gave Chievo the lead in the 17th minute, but Gonzalo Rodriguez equalised less than a minute later.
The closest either side came to winning it was when Luca Toni hit the post for Fiorentina just before half-time, but despite the chances, the game ended all square at 1-1.
Former coaching badge classmates Eugenio Corini and Vincenzo Montella had clearly studied each other two well as their sides cancelled each other out at the Bentegodi.
It was an open game, though, with the first chance coming in the seventh minute for the hosts when Luciano just missed the target with a volley from 10 yards out.
Fiorentina responded with a chance of their own in the 14th minute with Stevan Jovetic setting up Manuel Pasqual, but his well-placed shot was parried by Stefano Sorrentino, who was glad to see a defender on hand to clear the danger.
The home side took the lead three minutes later with Thereau sending his shot across Emiliano Viviano and into the far corner.
There was little time to celebrate before the Viola were back on terms.
Rodriguez latched on to Pasqual's corner, which was flicked on at the near post by Toni, and his touch struck the post on its way across the line, despite attempts by a Chievo defender to keep it out.
Chances continued to arrive at both ends with Toni coming closest to scoring a second just before half-time when he headed against the left-hand post.
After a more relaxed start to the second 45 minutes, Fiorentina nearly took the lead in the 55th minute when Juan Guillermo Cuadrado's low shot with the outside of his boot missed the far post.
Both Thereau and David Di Michele missed good chances for the hosts as the chances kept arriving as both teams threw caution to the wind.
But despite both teams' efforts, there was to be no winner as both Corini and Montella left with a smile having matched each other in their first encounter as Serie A coaches.