Leonardo Bonucci was the next Juventus player to come close to opening the scoring, although he was unable to guide his header towards the target following a cross into the box on 36 minutes.
Seven minutes before the interval, Juve midfielder Claudio Marchisio struck the post with a fine strike from the edge of the box, which had Abbiati beaten only for the frame of the goal to come to his side's rescue.
Both sides came into this game unbeaten in the league, and they pressed in the second half for a breakthrough goal with Stephen El Shaarawy coming close to finding one 10 minutes after the restart with a blocked strike from close-range.
The Old Lady did edge ahead on 71 minutes, however, courtesy of Carlos Tevez's strike which found the bottom corner of the net after Paul Pogba had picked him out.
Fernando Torres was introduced for the Rossoneri with 15 minutes remaining, but he was unable to help Milan find a leveller as Juventus held out for victory.