Second-placed Atalanta moved up to 75 points with two games left to play, while Juventus can win the Scudetto for the ninth successive season if they beat Sampdoria at home on Sunday. Juve also have a game in hand.
Atalanta coach Gian Piero Gasperini, who was serving a one-match touchline ban after being sent off during Tuesday's 1-0 win against Bologna, watched from the stands as his side fell behind to a moment of genius from Hakan Calhanoglu.
The Turkish winger sent a vicious dipping free kick sailing over keeper Pierluigi Gollini, who got his fingertips to it but could not keep the ball out in the 14th minute.
Atalanta earned the chance to equalise when the video assistant referee (VAR) ruled that Ante Rebic had stamped on Ruslan Malinovsky, but the Ukrainian struck his spot kick at a perfect height for Gianluigi Donnarumma to save.
The visitors levelled through Duvan Zapata, who out-muscled Davide Calabria to slot it home in the 34th minute, but despite that being their 96th league goal of the season, there was little sign of their usual firepower.
Instead, it was Milan who came closest to getting a winner as substitute Giacomo Bonaventura struck the foot of the left-hand post with a second-half shot that bounced off Gollini and almost ended up in the net.
As the clock ticked up towards 90 minutes, Milan had a late shout for a penalty when striker Zlatan Ibrahimovic appeared to be bundled to the ground, but the referee waved away their appeals.
"It is not easy to win these games, they are very balanced. In this heat and after all these consecutive games ... fatigue took over a bit," Gasperini told reporters.