Jose Mauri's goal was enough for the Gialloblu to make it seven points from its last three games, and 16 for the season, while at least delaying the Bianconeri's march to a fourth straight league title.
Juve's lead at the top of the table could be cut to 11 points this weekend, although it was clear that its focus had already shifted to a more important appointment in the UEFA Champions League on Wednesday morning (AEST) as Massimiliano Allegri made wholesale changes.
But that should take nothing away from Parma as it followed up its draw with Inter Milan and win over Udinese with another three points.
Genoa left Cagliari even deeper in relegation danger with a 2-0 win at the Stadio Luigi Ferraris.
Goals from M'Baye Niang and Iago Falque earned the Rossoblu all three points against a luckless Cagliari side, which hit the woodwork three times.
The win keeps Genoa in with an outside chance of making Europe next season, although Cagliari's hopes of staying up took a blow with five points separating it from Atalanta above the relegation zone, and the Bergamo club has a game in hand.
Inter Milan picked up a morale-boosting 3-0 win at Hellas Verona to revive its slim hopes of qualifying for Europe next season.
Mauro Icardi, Rodrigo Palacio and an own goal from Evangelos Moras earned the Nerazzurri its first victory since 23 February, ending a run of five games without a win and taking it to within six points of sixth-placed Napoli.
