The stalemate between the two heavyweights on Saturday could leave Juve nervously looking over their shoulders at the end of the weekend. They stay third, 11 points above seventh-placed Atalanta, who have two games in hand.
Injury-hit Milan are five points above Juventus, with the top five in Serie A qualifying for next season's Champions League.
Lazio moved to sixth and within three points of fifth-placed Roma, who play Napoli on Sunday, with a 1-0 win over relegation-threatened Hellas Verona.
Juventus, coming off draws against Torino and Cagliari, have now won just two of their past 13 Serie A matches.
Milan have also lost three of their past five in all competitions and endured the humiliation of losing to Inter on Monday, confirming their city rivals as Serie A champions.
Behind a decimated Milan defence, weakened by suspensions, stand-in Marco Sportiello was definitely the busier of the goalkeepers and did well to fingertip Dusan Vlahovic's free kick round his left post on the stroke of halftime.
Sportiello did even better after the restart with a fantastic double save to parry, first, a Filip Kostic attempt and prevent Danilo from tapping in the rebound.
He also kept out Weston McKennie's header minutes from the end, with Milan defender Malick Thiaw clearing Adrien Rabiot's follow-up off the line.
Lazio and former Verona midfielder Mattia Zaccagni again scored against his old club, just as he did in their first match this season.
Zaccagni started and finished the move in the 72nd minute, winning the ball on the halfway line, racing forward and rolling the ball across to Luis Alberto, who threaded it back for him to fire in at the near post.
Lazio winger Pedro, guilty earlier of a glaring miss, hit the post with a late free kick as Verona remained three points above the drop zone.
Lecce took another small step towards safety after drawing at home to Monza 1-1 with both goals in stoppage time.
Nikola Krstovic thought he'd secured third straight Lecce win when he scored in the second minute of stoppage time, but Matteo Pessina levelled from the spot after Lecce defender Lorenzo Venuti handled in the box.
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