An eventful Serie A match also saw both sides miss penalties.
Fiorentina dominated the opening exchanges and took the lead after 19 minutes when centre-back Facundo Roncaglia advanced unchallenged before launching a long-range shot that flew into keeper Antonio Mirante's top right-hand corner.
Parma responded and 10 minutes after the goal nearly equalised when unmarked Alessandro Lucarelli could only head Dorlan Pabon's corner against the post.
Fiorentina could have doubled their lead six minutes later when Roncaglia hit the post when he met a Matias Fernandez free kick only six yards out. Early in the second half Roncaglia clumsily ran straight through the back of Pabon to concede a penalty but Valdes lamely rolled the ball into the grateful arms of Emiliano Viviano.
Stevan Jovetic could have sealed the result for Fiorentina from the penalty spot with three minutes left when Mattia Cassani was brought down when clean through on goal by Rosi who received his marching orders.
However, Jovetic tried to clip the ball straight down the middle and saw his shot saved by Viviano's legs.
In a breathless finale Carvalho Amauri forced a superb save from Viviano and then a handball by Luca Toni allowed Valdes the chance to equalise from the spot.
He duly converted to send the home fans into raptures and leave Fiorentina still looking for their first away win of the season.
- Facundo Roncaglia
- Dorlan Pabon