The Argentine struck his second league goal of the season, his fourth in all competitions, after a superb pass from Paul Pogba, leaving Christian Abbiati on the floor as he fired home from close range in the 71st minute.
Tevez had not featured much in the earlier proceedings but Juve went close on a number of occasions through Roberto Pereyra, Giorgio Chiellini and Fernando Llorente.
Like in their victory over Malmo in the UEFA Champions League Massimiliano Allegri's side needed to be patient to maintain their 100 per cent start in all competitions.
Nigel de Jong paid particularly close attention to Tevez but, like his team-mates, he remained patient and when his opportunity came he took full advantage to devastating effect.
"There weren't many opportunities today because De Jong was always waiting for me," he told Sky Sport Italia.
"We expected a game like this, as Milan were coming off two wins, but we had confidence and were always in the match
"I managed to score eventually and I am happy."
Juventus remain top of the table after the win and are yet to concede a goal in their three Serie A matches so far this season.