Morata, who also scored last time against Malmö in the Champions League group game, got a pass at the center line early in the match and sprinted away on a solo run that lasted all the way and was crowned with a chip in the net behind the Milan goalkeeper.
Milan pressed for a draw in a match that was both physical and entertaining, despite the fact that additional goals shone for a long time with their absence.
But in the 76th, the dividend came on a corner.
Franck Kessie was behind the strike, which landed perfectly on Ante Rebic's forehead and via the post in goal.
Rebic, who incidentally acted as a replacement for an injured Zlatan Ibrahimovic, at the top of Milan's starting eleven.
The cross means that Juventus' cancer in the league continues and the team has so far not taken any three points this season.
The second Swede of the match, Dejan Kulusevski, started on the bench for Juventus but was substituted in the 78th minute of the match.
Thanks to the score, Milan went up to the same score, 10, as the leading Milan rival Inter.