The Montenegrin forward tapped home from close range after the ball broke to him in the seventh minute.
Luca Toni also had an effort ruled out for offside as the hosts dominated proceedings.
The win lifted Fiorentina to the verge of the European places with Bologna still in mid-table.
The Viola took the lead early on when Matias Fernandez's cross took a deflection off Nenad Tomovic and fell to his team-mate Jovetic to score with ease.
Jovetic tried his luck with a lob which dropped just over, while Fernandez's cross-shot was tipped over the crossbar by Bologna goalkeeper Federico Agliardi.
The visitors finally got a sight of goal in the 37th minute as Alessandro Diamanti drilled just wide from long range.
Toni was denied by the offside flag five minutes into the second half, knocking home the rebound after Agliardi had punched away a shot from Manuel Pasqual.
The one-way traffic continued as Fernandez fired a 25-yard free-kick over the bar and Jovetic also shot high from outside the area.
Juan Cuadrado then beat his man as he cut inside from the left to bring a save out of Agliardi, but the home side had to settle for a solitary goal.