For long periods Carlo Ancelotti`s side looked to have claimed the points, following a superb first-half strike from Gianluca Zambrotta.
However, Baggio raced clear of his markers and showed instant control to take the ball out of the reach of Juve keeper Edwin van der Sar before slotting into an empty net.
Filippo Inzaghi thought he had immediately restored Juve`s lead, but his effort was ruled out for offside.
Zambrotta will be hugely disappointed that his goal did not claim the points, as his effort was worthy of winning any game.
He controlled a deep Alessandro Del Piero corner before volleying past Pavel Srnicek from the edge of the box.
However, Baggio had the last word against his former club, a result that was made worse for Juve following Roma`s 3-1 home win over Verona.
Roma took full advantage of their nearest challengers` slip to move nine points ahead in the title race thanks to a 3-1 win over Verona in Rome.
A brace from Vincenzo Montella and a goal on his return from injury by Gabriel Batistuta helped Fabio Capello's men overcome a visiting side that had taken a 1-0 lead into the break courtesy of Mauro Camoranesi's 27th minute goal.
Former Manchester United goalkeeper Massimo Taibi was the hero of the day in Serie A. The Reggina captain popped up to score a dramatic late equaliser for Reggina in a 1-1 draw with Udinese.
Taibi's first ever goal brought Reggina level after Udinese's Brazilian defender Alberto had given the visitors the advantage.
A Christian Vieri hat-trick was the highlight of the day in Serie A as ten-man Inter won 3-2 at Perugia.
Vieri grabbed two second-half goals after Inter had been reduced to ten when Laurent Blanc was dismissed after picking up his second booking in the 49th minute with the score locked at 1-1.
Earlier Perugia's Inter-bound defender Marco Materazzi scored against his future employers a minute before the break to cancel out Vieri's opening goal on 22 minutes.
Zivis Vryzas gave the score more respectability with an injury time consolation for Perugia.
Fabio Pecchia gave Napoli a half-time lead at Atalanta but Cristiano Doni secured a point for the home side with a 69th minute penalty.
Paolo Cannavaro, younger brother of Italian international Fabio, was dismissed near the end of Parma's disappointing goal-less draw at home to Bologna.
Parma coach Renzo Ulivieri bemoaned the recent international week, saying: "We have not played good football this afternoon and I think that we did not have a good training session in the last two weeks because of international matches."
Bologna coach Francesco Guidolin is eyeing a Uefa Cup spot, saying: "Bologna cannot target the Champions League, but I want my players to give their best in the last few matches of the season because I want a Uefa Cup place."
