Ronaldo turned the ball towards goal with his right foot but his left heel blocked the shot which then rebounded into the path of Mandzukic who swept it home.
Juve have now won their opening two matches after last weekend's 3-2 victory over Chievo in Verona.
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. "I'm happy with how he's fitting in, he is a very humble lad".
Ronaldo joined Juventus from Real in a £99.2million this summer, ending a remarkable nine-year spell with the Spanish side which yielded eight major trophies and five Ballon d'Ors.
"We did not expect this start, we wanted a different calendar", said Lazio coach Simone Inzaghi blaming "basic errors" after defeats against the top two teams.
However, he touched the ball only once in the Lazio penalty area in the first half and, shortly before Juve's second goal, had a dipping shot superbly tipped over by Thomas Strakosha.
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.More news: Oil rises as China demand resumes, signs that Iran supply curbed
'We must give something more because otherwise we can not get better results.
Juventus went 2-0 up 15 minutes from time when Mandzukic was on hand to tuck into an empty net after Ronaldo made a mess of an attempt at goal.
"Of course we're going to help him, we're going to help him score goals".
"For example, the wing is more covered with Douglas Costa, but we also know what can happen with CR7 there".
Ronaldo's accidental assist sparked plenty of debate between football fans. Of course, we will learn from his game.
The win took Napoli, last season's runners-up, level with Juven on six points.