Ronaldo will claim the headlines, but Costa will be under intense scrutiny in the coming days and weeks after three appalling incidents in the closing minutes of the game.
"I am very happy to have scored my first double with the jersey of Juve and especially to have contributed to this important victory of the team", Ronaldo tweeted. "I'm happy. I'm working hard and my teammates are really helping me adapt to this league".
Ronaldo, goalless in his first three games since his move from Real Madrid, tapped in shortly after half-time.
His first, in the 50th minute, was probably the worst goal he's ever scored, before he followed it up with an emphatic left-footed finish to take him to 400 league goals in his career.
Cristiano Ronaldo celebrates after scoring his second goal on Sunday.
With Juve set to kick their Champions League campaign off against Valencia this Wednesday, this is exactly the sort of form they want Ronaldo in.
Douglas Costa was then sent off after spitting at Federico di Francesco, with the Brazilian winger also appearing to aim a headbutt and elbow his opponent.
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The five-time Ballon d'Or victor was denied a hat-trick by a fine save from Sassuolo goalkeeper Andrea Consigli, while he also miss-hit a clear opportunity late on.
Victory helped Juve maintain their ideal start in Serie A, and while the match was marred by a Douglas Costa spitting incident, Ronaldo revealed his relief at rediscovering his goalscoring boots.
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Just after Costa was given a yellow card for locking horns with Di Francesco, the two bickering players came together again and Costa elbowed his rival and than spat at Di Francesco's face.
This is Costa's first full season at Juventus after the club paid a €40 million transfer fee to make his loan move to Turin permanent.
Inter Milan's woes were compounded with a shock 1-0 home defeat by Parma on Saturday ahead of their European opener against Tottenham at the San Siro.