With Milan six points clear of third-placed Juve, they knew they had to win in Brescia to put some pressure on the UEFA Champions League holders - who face Sampdoria on Sunday.
It looked they were going to slip further behind the leaders as Stefano Mauri gave the hosts the perfect start by scoring against Marcello Lippi's side after just three minutes.
Andrea Caracciolo made matters worse for the visitors when he doubled Brescia's advantage six minutes before the break to send them in 2-0 up at half time.
Lippi's team bounced back in the second half and Fabrizio Miccoli pulled a goal back from the penalty spot on 53 minutes.
Marco Di Vaio then levelled matters two minutes later and as the pressure mounted, Juve grabbed a winner 15 minutes from time through Czech star Nedved.
The Turin side are now second, three points behind Milan but having played a game more.
Elsewhere, Parma also left it late as they had to come from behind twice to grab a 2-2 draw at Modena.
Matteo Pivotto gave the hosts the lead two minutes before the interval but Alberto Gilardino equalised from the spot on the stroke of half time.
Maurizio Domizzi restored Modena's lead on the hour but Matteo Ferrari grabbed a point for Parma three minutes before full time.
Match Summaries:
Brescia v Juventus
Modena v Parma
