As Toldo and his Argentine teammate missed the ball, Filippini was quick to kick it into the open net.
Filippini, an amateur guitar player and a fan of Bruce Springsteen, celebrated his goal using the corner flag as a guitar.
Parmalat, the diary and food conglomerate owned by the Tanzi family and Parma's main commercial sponsor, was involved in a multibillion dollar scandal that will force the group to unload the club.
"We managed to outplay Inter with quick actions and a lot of determination," Parma coach Cesare Prandelli said.
Inter's second loss in its last three matches was likely to hurt its title chances. Inter trails leader AS Roma by five points ahead of Sunday's 16th-round matches in Italy's top league.
Stefano Tanzi, the son of the disgraced Parmalat founder who resigned as president of Parma Calcio on Friday, was at the stadium to support the team.
Parma fans ignored him as the 13-year-old team ruling by the Tanzi family eventually ended this week with the announced resignation of the younger Tanzi and of the entire club board.
However, Prandelli said he and the players dedicated victory to the former club president.
French League
Paris Saint-Germain climbed to second place in the French first division, following a scrappy 1-0 home win over battling Lille.
The win, achieved on an own goal by Lille's debutante Greek defender Stathis Tavlaridis in the 13th minute, moves PSG onto 38 points -- three clear of third-place Lyon, but seven behind leader Monaco.
Monaco beat Lyon 3-0 in a crunch match played Friday, with captain Ludovic Giuly scoring twice.
Marseille 'keeper Fabien Barthez played his first league match since joining on loan from Manchester United but was powerless to prevent a 2-0 away loss to Auxerre.
Auxerre's win, secured on goals from Teemu Tainio and Bonaventure Kalou, moved it up to fourth place on 35 points, just ahead of Sochaux and narrowly behind Lyon on goals difference.
Sochaux, in fifth spot, could not break down seventh-placed Nice's stubborn rearguard and settled for a 0-0 home tie. Marseille's loss means it stays in sixth position.
Bordeaux climbed to eighth place following a 2-1 away win at Montpellier. Marouane Chamakh and Rio Mavuba scored for the visitors, while Portuguese striker Rui Pataca notched Montpellier's consolation goal.
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