"I wanted to score, I'm really happy, " said Ronaldo, who had missed several good chances in previous games.
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.
Ronaldo scored the first goal with an easy tap-in while another one came through his trademark finish from distance.
The five-time Ballon d'Or victor missed out on a couple of gilt-edged chances in the second half to grab his first hattrick for his new employers but nonetheless finished the encounter delighted by breaking his mini goal drought. "I hope we get a bit of luck".
Juventus get their Champions League campaign underway on Wednesday as they travel to Spain to take on Valencia. With both goals coming from Cristiano Ronaldo, manager Massimiliano Allegri will not be overwhelmingly pleased, however, as footage emerged of Douglas Costa unmistakably spitting at an opponent.More news: Samsung Teases Mysterious '4X Fun' Galaxy Event on October 11
Costa later apologised for his late red card for elbowing and spitting at Di Francesco - the 24-year-old son of Roma coach Eusebio Di Francesco.
But Valter Birsa reduced the deficit shortly after the break with a magnificent curled strike and Chievo equalized seven minutes from time when Mariusz Stepinski fired in a rebound.
Winless Chievo are on minus one point after having three deducted on Thursday by the Italian federation over accounting irregularities.
Former Juventus defender Patrice Evra replied to Costa's post by saying: "You know that the symbol of Juventus is a zebra and not a llama".
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.