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Torino Relegate Parma - Getty Images
Mergim Vojvoda tapped home the winner midway through the second half to leave Parma 12 points away from 17th-placed Cagliari with four games to play, but with an inferior head-to-head record that makes it impossible for them to escape the drop zone.
For hosts Torino, meanwhile, it was a precious three points in their battle against the drop which moved them up to 15th, three points away from Benevento who occupy the final relegation place.
During the 1990s, Parma were among the top sides in Italy and a force in Europe, winning the Uefa Cup in 1995 and 1999 and Cup Winners Cup in 1993.
A financial collapse led to relegation from Serie A in 2015 and rebirth in the semi-professional Serie D, Italian football's fourth tier.
Three straight promotions took them back to the top flight but they failed to establish themselves as a force and drop down to Serie B.