The 33-year-old failed to find the net in his first three Serie A matches following a €112m transfer from Real Madrid in July before finally breaking his duck on Sunday, goal.com reported.
He scored from close range after 50 minutes to break the deadlock and then followed up with a second 15 minutes later, angling in a drive to secure the points for Massimiliano Allegri's men.
Ronaldo praised the way Juventus broke down a stubborn visiting defense and admitted that his failure to find the net had been starting to play on his mind.
"I'm very happy, we started well," he told Mediaset.
"Sassuolo defend well, but we put in an intense performance and deserved to win.
"I really wanted to score these first goals and I'm happy to have found the net.
"This is football. The important thing is that the team wins. Obviously, I was a little tense with all the talk of Real Madrid and not scoring, but I thank my teammates for supporting me throughout.
"I knew that I was working well and it was only a matter of time. I am adapting well to Italian football."
Juventus travels to Valencia for its opening Champions League fixture on Wednesday and Ronaldo is looking forward to playing again in a competition he has won three times in the last three years with Madrid.
Manchester United and Young Boys are also in Group H and Ronaldo acknowledged that a tough task lies ahead for Juventus, which reached the quarterfinals last season.
"The Champions League is my favorite tournament," he said.
"It's a very difficult group, we know that we can do well and Juve must focus on being the best."