An Adem Ljajic penalty and Lorenzo De Silvestri deflected effort gave Fiorentina their first win of the campaign.
The Viola were in dire straits and penultimate place without a single victory. Only Sebastien Frey's heroics earned a point at Genoa midweek, while in their last home outing they were booed off the field following a 2-1 defeat to Lazio.
Manuel Pasqual joined Stevan Jovetic and Gaetano D'Agostino on the injury list, while Riccardo Montolivo played with the aid of painkilling injections. Parma missed Sebastian Giovinco, Alberto Paloschi and Daniele Galloppa, so Antonio Candreva took the trequartista role.
The Ducali won here 3-2 last season, but within 20 seconds Adem Ljajic had forced a desperate save out of Antonio Mirante.
Ljajic also fired wide under pressure from Massimo Paci, then at the other end Frey had his gloves stung by a Massimo Gobbi blockbuster.
Mirante was again crucial to deny Alberto Gilardino after a fine passing move set up by Juan Manuel Vargas, then smothered an Alessio Cerci solo effort.
Fiorentina were fortunate when Lorenzo De Silvestri missed a seemingly easy cross, but Marques wasn't expecting it either and didn't get the tap-in.
Parma have given away a penalty in every game this season and this time it was Alessandro Lucarelli who dragged back Gilardino as he tried to get on the end of a Vargas cross. Ljajic took the spot-kick duties and calmly rolled it through the middle with the inside of his foot.
De Silvestri put the points under lock and key for Fiorentina's first win of the season. The full-back's shot took a decisive deflection off Lucarelli to loop over the goalkeeper and slot into the near top corner.