Ronaldo, five-times World Player of the Year, opened his account in the easiest possible fashion by tapping into an empty net from less than two metres in the 50th minute before finishing off a counter-attack to claim his second.
Khouma Babacar headed one back in the 90th minute but the game ended in ugly scenes as Costa became involved in a running feud with Sassoulo midfielder Federico Di Francesco.
The Brazilian escaped with a booking for elbowing and head-butting his rival as they tangled before the Sassuolo goal, but was sent off after cameras caught him spitting at the same player in another altercation.
Amid much less fanfare, Argentina forward Gonzalo Higuain, who left Juventus on loan shortly after Ronaldo’s arrival, scored his first goal for AC Milan to earn them a 1-1 draw at Cagliari.
AS Roma warmed up for their visit to Real Madrid on Wednesday by squandering a 2-0 lead and drawing 2-2 at home to lowly Chievo.
Juventus, chasing an eighth successive Serie A title, have 12 points, three ahead of Napoli, while Sassuolo are on eight after their first defeat of the season.
“I was a little bit anxious as expectations were high,” Ronaldo said. “I really wanted to score, so I’m happy.”
Sassuolo allowed Ronaldo few openings in the first half apart from an early shot which was blocked and a header wide from Alex Sandro’s cross.
He also tried his luck from a 30-metre free kick, sending a disappointing effort harmlessly wide of Andrea Consigli’s goal.
But Juve coach Massimiliano Allegri’s prediction that it would be Ronaldo’s day proved to be right.
Ronaldo’s luck changed when Sassuolo defender Gian Marco Ferrari headed a corner on to his own post and the rebound left Ronaldo with the easiest of tap-ins.
Sassuolo, who caused Juventus trouble all afternoon, were then caught on the break, with Emre Can sliding the ball to Ronaldo to drill an angled left-foot shot into the far corner.
Ronaldo could easily have had a hat-trick but missed two more good chances and had a penalty appeal turned down.