The 33-year-old forward has scored 12 goals since leaving Real Madrid in the offseason, despite being the subject of a rape allegation in the United States.
Gonzalo Higuain and Hakan Calhanoglu both missed chances for Milan.
Juventus thought it doubled its lead but Mandzukic's effort after Ronaldo nodded on a free kick was ruled out for offside.
Juventus have an 11-point lead over second-placed Napoli, who hosts lowly Frosinone on Saturday.
Allegri gained 17 votes for the Panchina d'Oro (Golden Bench) award, beating Napoli's Maurizio Sarri, now at Chelsea, and Lazio's Simone Inzaghi, who gained eight votes each.
It was Ronaldo's first goal in six matches at San Siro, having previously played at the iconic stadium for Manchester United and Real Madrid.
Ronaldo may not have found the net for Juventus in the 3-1 win over Cagliari, but the Portugal international has helped his new club win 10 of its opening 11 league games.
Ronaldo scored twice as Juventus came from behind to win at relegation-threatened Empoli 2-1 on Saturday and maintain their unbeaten start in Serie A.
Inter star player Nainggolan hurt his ankle in a crunching tackle with Lucas Biglia in the first half. The Belgian midfielder will undergo tests on Monday but is now a doubt for Champions League match at Barcelona.
Ronaldo scored Juventus' second goal in a 2-0 win at Udinese to extend the Bianconeri's perfect start in Serie A.
Mandzukic has four goals in six appearances, he scored only five in 32 league games last season and is working well with Ronaldo in a three-pronged attack, with Paulo Dybala dropping back.
Ronaldo set up all three of his side's goals — two for Mario Mandzukic and one for Leonardo Bonucci — as Juventus opened up a six-point lead over Napoli.
It was Ronaldo's third goal in two Italian league games after the Portugal star took a while to get off the mark for his new club following his move from Real Madrid.
It took the former Real Madrid forward nearly 320 minutes to score his first league goal for Juventus and he did it with the simplest of tap-ins.
The 31-year-old Khedira is in his fourth season at Juventus, and he has played more minutes than any other midfielder at the club in his first three seasons.
Ronaldo was also visibly upset when Mandzukic prevented the Portugal captain from connecting on a volley early on by getting there first, prompting an apology from Mandzukic.
Ronaldo left Real Madrid in the offseason in a Serie A record 112 million euro (then $132 million) deal but has yet to fully adapt to Italian football.
Ronaldo moved from Real Madrid to Juventus in the offseason in a Serie A record 112 million euro (then $131.5 million) deal.
Cristiano Ronaldo took just eight minutes to score his first for Juventus, in the traditional pre-season friendly against the team's "B'' side on Sunday.
Ronaldo made Juventus fans wait only eight minutes before scoring his first goal for the club in a traditional pre-season friendly.
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