Fiorentina have 45 points, five adrift of Napoli who occupy the final Champions League qualifying place in third and were hosting mid-table Genoa later on Monday (2000 GMT).
Parma's Antonio Cassano fired in from close range to give the hosts the lead after 39 minutes and Juan Cuadrado levelled two minutes later for fourth-placed Fiorentina.
Parma, who are seventh on 37 points, regained the lead six minutes after halftime with a controversial penalty awarded for a high challenge by Nenad Tomovic on Jonathan Biabany and converted by Amauri.
Fiorentina, already seething over that decision, were further aggrieved two minutes later when Modibo Diakite was sent off for a second bookable offence after a foul on Cassano.
There was more trouble in stoppage time when Parma were awarded a free kick outside the Fiorentina penalty area and a scuffle broke out as the visitors tried to organise their wall.
Fiore playmaker Borja Valero and Parma substitute Gianni Munari, who had only been on the field for 10 minutes, were sent off for lashing out.
(Reporting by Brian Homewood; Editing by Ken Ferris)
