Pjanic converted spot-kicks either side of the break, while Valencia's Dani Parejo saw his penalty saved by Wojciech Szczesny in stoppage time.
It was Ronaldo's first red card in 154 career Champions League matches.
Juventus forward Cristiano Ronaldo (L) reacts next to teammate Federico Bernardeschi after receiving a red card during the UEFA Champions League group H football match between Valencia CF and Juventus FC at the Mestalla stadium in Valencia on 19 September, 2018.
Ronaldo tussled with Jeison Murillo and appeared to put his hand on the centre-back's head in the 29th minute inside the box, with the official behind the goal signalling for an offence.
"The only thing I can say is that VAR could have helped the referee make the right decision", said Juve coach Massimiliano Allegri, lamenting the lack of video technology in UEFA tournaments.
Ronaldo looked baffled and kept protesting his innocence, briefly laying on the ground to express his disbelief.
Despite playing more than an hour with 10 men at Valencia, Juventus eased to victory.
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However, ESPN has been told it is unlikely that Ronaldo will receive any extended ban on top of the automatic one-game suspension.
Ex-England midfielder Owen Hargreaves discussed Ronaldo's reaction to the red card on BT Sport after the match, with the former Bayern Munich player highlighting the star's emotional reaction to the referee's decision.
Brych did not see the incident, but was called over by his goal-line assistant Marco Fritz.
Ronaldo's red card will mean he is likely to miss Juve's clash against his former club Manchester United who they face in the third round of fixtures.
After seeing Ronaldo's infraction, it's tough to believe that he'd be suspended for two matches.
The Spain defender's dubious record aside, it was a spectacular start to the three-time defending champions title defence, with Gareth Bale, Isco and returnee Mariano all scoring, the latter's tally his first-ever in the Champions League.
Juventus host Young Boys next in the competition before two straight games against United, with the first match at Old Trafford on October 23.