Andrea Pirlo gave Juventus the lead with a trademark free kick early in the second half but Nicola Sansone leveled in the 78th minute to preserve Parma's unbeaten home record.
Second-place Lazio is now only three points behind Juventus after recording a controversial 2-0 win at home to Atalanta.
It is a blow for Juventus, which had an eight-point advantage at the start of the year.
Former Atalanta striker Sergio Floccari gave Lazio the lead after the ball struck his arm, and an own goal from Davide Brivio sealed the result.
Napoli is two points further back after cruising to a 3-0 win at home to Palermo. Fifth-place Fiorentina surprisingly lost 3-1 at Udinese as Antonio Di Natale scored twice.
Juventus was eager to get back to top form after a loss at home to 10-man Sampdoria last week and a narrow extra-time victory over AC Milan in the Italian Cup.
However, Parma is the only team left in Serie A yet to lose a game at home.
Parma dominated the early stages but Juventus slowly began to get into the game and Pirlo sounded a warning shot at the end of the first half with a free kick which Antonio Mirante did brilliantly to keep out.
Pirlo had scored four goals this season, all from direct free kicks, and he added to his tally when his effort was deflected off Jonathan Biabiany in the wall and completely wrong-footed Mirante.
Parma leveled on the counter attack when Gabriel Paletta sent a great ball throught to Sansone who raced clear of Martin Caceres before slotting it past Gianluigi Buffon.