Stuttgart made another mistake just before the end when Josha Vagnoman attempted to play the ball back to keeper Alexander Nübel, only for Kingsley Coman to intercept it and slot it in from distance to score Bayern’s third.
Bayern turned the match around in the 64th minute when a quick-thinking Leon Goretzka intercepted the ball from a defender inside the box and calmly slotted it home to give the leaders a 2-1 lead.
Fiorentina should have made sure of the victory after 73 minutes but Lucas Beltrán’s penalty, given after a handball in the box, came back off the upright.
Bayern Munich fought back from a goal down to maintain their place at the top of the Bundesliga with a 3-1 victory at Stuttgart.
The win keeps Bayern comfortably atop the Bundesliga with 61 points, 11 more than Bayer Leverkusen, though they have played one match more.