The referee consulted his assistant behind the goal and chose to show Ronaldo a straight red card, with the contact he made with Murillo's head likely to be the reason for the sending off.
Ronaldo may now be suspended for Juventus' match against Manchester United at Old Trafford on matchday 3 of the group stage.
Ronaldo is the competition's highest scorer with 120 goals and will have to wait until matchday four, when Juve host Manchester United, for a chance to open his European account for his new club.
The Italian champions will host Swiss side Young Boys in their next group game at the Allianz Arena on October 2 as they now rank second on Group H table behind Manchester United - but on the same points.
Pogba then set up the third 20 minutes into the second half, laying the ball into the path of Anthony Martial, whose deflected the goalkeeper David von Ballmoos to score his first goal for United since Alexis Sanchez joined the club.
And Juventus boss Massimiliano Allegri said after Wednesday's game: "VAR would've helped the referee in this decision".
Cristiano Ronaldo arguably is the best player in UEFA Champions League history and led Real Madrid to the last three titles in this competition.
The Juventus superstar was sent off with a straight red card in the 29th minute against Valencia for a foul against defender Jeison Murillo.
However, his consolation will be that Juventus was cruising to a crushing victory against the Spanish team, despite being reduced to 10 men.
Referee Felix Brych did not hesitate in bringing out the red card to mark an end to Ronaldo's night after 28 minutes.
[MarinoPeixoto]Cristiano Ronaldo getting a red card on his European debut for Juventus might not be fair but it certainly is amusing.