Ronaldo, 33, played a role in Mandzukic’s second goal of the night on 75 minutes after Pjanic put the hosts in front at the Allianz Stadium.
The five-time Ballon d’Or winner joined the Serie A champions from Real Madrid on July 10 in a 100-million-euro deal but has yet to score his first competitive goal.
Juve have now won their opening two games after last weekend’s 3-2 success against Chievo in Verona.
Lazio — fifth last season in Serie A — have had their worst start to the season in over a decade following last weekend’s 2-1 defeat at home against Napoli.
In the first home game for the seven-time defending champions, Paulo Dybala and Douglas Costa started on the bench, with coach Massimiliano Allegri opting for Federico Bernardeschi and Mandzukic to spearhead the frontline with Ronaldo.
Simone Inzaghi’s Lazio had ended Juventus’s two-year unbeaten home Serie A run last year, but apart from a Luis Alberto shot after an hour they failed to threaten.
Germany international Sami Khedira rattled the woodwork after 19 minutes for the home side, with Lazio goalkeeper Thomas Strakosha diving to keep out a Bernardeschi angled drive.
But the hosts broke through on the half-hour when Mandzukic knocked down a cross for Pjanic to power a half-volley into the corner.
Lazio’s Marco Parolo missed a chance to equalise when his header flew over the bar just before the break.
Ronaldo came close after 63 minutes but headed just wide after connecting with a Joao Cancelo cross and again threatened on 71 minutes but Strakosha tipped over.
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.
It was the first time that Ronaldo has not scored at the Allianz Stadium, having found the net three times for Real Madrid against the Italians.
Ronaldo’s next chance for his first goal will come against promoted Parma next Saturday.
Meanwhile, Carlo Ancelotti faces an emotional home debut as Napoli coach against old club AC Milan later on Saturday.
Ancelotti spent most of his career at AC Milan with the 59-year-old winning three Serie A and four European titles as a player and coach with the northern giants.