With Roma only managing a 0-0 draw at home to Inter on Saturday, Antonio Conte's men stretched the gap at the summit to 11 points, though Juventus have played a game more.
Juve's San Siro triumph was not without complications, as Milan enjoyed concerted pressure for the majority of the first half.
But Fernando Llorente's tap-in on the stroke of half-time put the hosts ahead, before Tevez extended the lead with a fierce strike that hit the underside of the crossbar before nestling in the back of the net.
Juventus have now gone 18 matches unbeaten in Italy's top flight, and Tevez stressed the importance of defeating Clarence Seedorf's men.
"(The) win was so important," he told Sky Sport Italia. "We knew that Roma hadn't won against Inter and it was important to get three points - even if this match was worth more than that."
On his goal, he added: "The ball dipped very sharply, that's what stopped the goalkeeper from saving it."
Strike partner Llorente was also thrilled with the hard-fought win, though the Spaniard was thankful to an improved second-half showing from the defending Serie A champions.
"It was a difficult game," he added. "They played well in the first half, putting us under pressure throughout.
"We didn't expect it and struggled, but in the end we put together a nice move for the first goal and then regrouped in the second half, when we played better. (We) deserved the victory and gained three golden points."
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