Miralem Pjanic rifled Juventus ahead in the 30th minute with a shot from outside the area before the Turin side added a second in the 75th minute in untidy fashion.
As pointed out by several people, the forward didn't score a goal in his first three games of the La Liga season a year ago and got just one goal in his first eight games.
Ronaldo nearly sensationally doubled the Old Lady's lead 20 minutes before time with a dipping strike from just outside the box but Lazio shot-stopper Thomas Strakosha made a superb save to tip the strike over the bar. His debut, however, proved to be a hard one against Lazio who finished fifth in the Serie A and level on points with fourth-placed Inter Milan last season.
The closest Ronaldo came to breaking his duck was with a vicious dipping effort on the turn in the 71st minute which was brilliantly turned over the bar by the Albanian goalkeeper.
Juventus goalkeeper Wojciech Szczesny, again preferred ahead of new signing Mattia Perin, made two key saves in the first half, turning Senad Lulic's shot around the post and then charging out of his goal to block a risky Marco Parolo break.
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They know the city, they know the club, they know the north east and how well you can stay here and leave here. We are very happy with him, so I think that, until January, he will stay with us.
Cancelo then set up Ronaldo for what looked destined to be his first goal for his new club, but the Portuguese star failed to control the ball in front of goal and Mandzukic fired home.
'That said, we will improve and I'm pleased because this is an important win in our first match against a direct rival. I'm delighted with how Ronaldo is settling in'.
'At times our play is too frenetic and at others we go to sleep, but we need to move the ball more quickly when the opposition tire.
"It was a different game to Verona [a 3-2 win at Chievo on the opening day]", Allegri told Sky Sport Italia.
Giacomo Bonaventura sensationally opened for Milan after 15 minutes in the San Paulo Stadium with a Davide Calabria half-volley giving the visitors a two-goal advantage four minutes after the break.