In July, Ronaldo had left Spanish club Real Madrid to join Juventus in a deal that cost over 100 million Euros.
Brazilian winger Costa already looked to have lost his composure after aiming an elbow and a headbutt moments earlier - but the worst was to come as he spat directly at Di Francesco from inches away.
Coach Massimiliano Allegri says he is not concerned that Ronaldo has failed to find the net despite 23 shots at goal in three games.
The 33-year-old's first goal came from a tap in after the ball struck the post, while his second saw him drill across goal and hit the far post.
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"This is football. The important thing is that the team win".
Ronaldo could easily have had a hat-trick but missed two more good chances and had a penalty appeal turned down.
"I also apologize to my teammates, who are always with me in lovely and bad moments".
Victory helped Juve maintain their flawless 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.
"I knew that I was working well and it was only a matter of time".
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"I'm very happy, we started well".
"I don't expect Ronaldo to do more or less than what he did in the first three games", said Allegri.
Ronaldo was delighted to get off the mark for his new club. "Even if I just gave him two passes, he would score two goals and that's why he's one of the greatest footballers who's ever lived".
The Argentine pounced in the second half, to score his seventh goal in eight games against Cagliari, and 112th in Serie A, coming close to a second from close range.
And Allegri indicated he wants to move on from the incident, with Costa still in his plans for Wednesday's Champions League opener against Valencia.
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