The Italian giants, stripped of their Serie A title in the summer and relegated for match-fixing, were expected to quickly make inroads into the 17-point penalty they also incurred.
And when Matteo Paro gave Juve the lead after 60 minutes it looked as if they would start their new era with a victory.
Moments later, Rimini's Domenico Cristiano was red carded for a foul on Pavel Nedved, one of several world-famous names to stay with the club.
However, with 15 minutes remaining Rimini delighted the crowd of 10,000 with a surprise equaliser.
Adrian Ricchiuti seized on a misunderstanding between Jean-Alain Boumsong and Robert Kovac and fired past World Cup winning goalkeeper Gianluigi Buffon.