- Giacomo Bonaventura (53')
Instead, Inter are third with 50 points, with fourth-placed AC Milan only two points behind and with a game in hand.
"There is great disappointment, we lost two consecutive home matches. We need to work more, starting with me," Inter manager Simone Inzaghi told DAZN.
"Fiorentina are a quality squad, the lads did all they could. It's just like this at the moment, we need to be more determined, because we had so many chances to score and we should've taken them."
The hosts missed a gilt-edged chance to go ahead after 20 minutes when Henrikh Mkhitaryan's shot from inside the box went straight at keeper Pietro Terracciano with the following overhead kick going into the side netting.
Fiorentina striker Jonathan Ikone also missed an opportunity seven minutes before the interval from point-blank range.
Romelu Lukaku could have sent Inter ahead four minutes into the second half but the Belgian failed to tap in a cross from six yards.
Giacomo Bonaventura was in the right place after a rebound from a corner and headed the ball into the net from close range to give Fiorentina the lead after 53 minutes.
Inter squandered a chance to draw level six minutes later, with Nicolo Barella's powerful half-volley from the edge of the box hitting the crossbar.
"The lads gave their all but obviously this is the 10th defeat of the season and that means something isn't working. This isn't where we wanted to be in the table," Inzaghi said.
Fiorentina, who have won five successive league matches, are eighth with 40 points.
- Fabio Maresca