Having also lost 2-1 at home to CSKA Moscow in the Champions League on Tuesday, the pressure was back on Inter who are struggling to recover from a dreadful start to the season under Gian Piero Gasperini's short-lived leadership.
They were helped at the San Siro by an insipid performance from the visitors, who were missing injured playmaker Stevan Jovetic.
Inter broke through four minutes before the break when Fiorentina were caught out by Coutinho's lobbed pass and Pazzini pounced to cleverly flick the ball past Boruc.
The former Fiorentina player chose not to celebrate the goal against the club where he spent four seasons.
Inter's win left them ninth with 17 points, one more than Fiorentina who dropped to 14th.
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