The Juve loss came three weeks after their 49-match unbeaten record ended with a 3-1 home defeat by arch-rivals Inter Milan.
For AC Milan, the win completed an impressive week in which the Rossoneri also sealed qualification for the knockout stages of the Champions League.
Former Milan striker Marco van Basten was a guest of honour at San Siro, though not, according to club vice-president Adriano Galliani, with an eye on replacing Allegri.
An unconventional-looking front three of Robinho, Stephan El Shaarawy and Kevin Prince Boateng, pushed up from midfield, combined well to inspire's Milan's win.
Juventus found it difficult to deal with Milan's pressing play and went behind just before the half-hour mark when the ball appeared to strike Mauricio Isla's outstretched arm from Antonio Nocerino's header, although replays suggested it hit the Chilean's body.
Robinho stepped up to score, despite keeper Gianluigi Buffon getting both hands to the ball.
The visitors were slow to react, with too many misplaced passes and errors allowing Milan to control the game.
Juve began to turn up the pressure later in the second half, with substitute Sebastian Giovinco, on for Fabio Quagliarella, going close with an overhead-kick from Simone Padoin's cross in the 62nd minute, but their lack of physical presence up front made life easier for the Milan back four.
The Italian champions attacked in numbers as the game entered its final stages, but Milan were increasingly happy to defend deep and try to catch Juve on the break.
It was a risky strategy and the home side lived dangerously at times, but worked hard to take all three points, putting a dent in Juve's title challenge and providing a possible platform for Milan to build on in the run up to the winter break.
Juventus will welcome coach Antonio Conte back from his touchline ban, imposed after being found guilty of failing to report attempted match fixes while coach of Siena, on December 8.
Angelo Alessio, Conte's deputy on the touchline, bemoaned his side's failure to match Milan's work rate.
"When we don't play as a team, we suffer and we lose, like we did tonight," he told Sky Italia.
Inter Milan now have the chance to close the gap on Juventus to just one point if they can win their game at Parma on Monday.
Earlier, Mounir El Hamdaoui came off the bench to score a late equaliser for Fiorentina at Torino, with a 2-2 draw enough to lift the Tuscans up to joint-second in the table.
The hosts took the lead five minutes from the break after Alessio Cerci got himself on the end of a low Danilo D'Ambrosio cross, with Riccardo Meggiorini's dummy fooling the Fiorentina defence.
Fiorentina came alive in the second half, but with talisman Stevan Jovetic still out injured and Luca Toni in the treatment room following a nasty collision with defender Kamil Glik, Torino were able to weather the storm.
The visitors drew level from the penalty spot in the 75th minute after D'Ambros
