Dejan Kulusevski and Alvaro Morata were also on target although it could have been very different if Juve's 42-year-old goalkeeper Gianluigi Buffon had not saved with his legs at close range from Juraj Kucka in the 15th minute.
Ronaldo's brace made the irrepressible Portuguese the league's topscorer, the 35-year-old moving two goals clear of AC Milan's Zlatan Ibrahimovic and Internazionale's Romelu Lukaku as he bounced back from his penalty miss against Atalanta on Wednesday.
Parma had the first real chance when a breakaway ended with the ball being played to Kucka at the far post but his effort was stopped by Buffon.
Juve, however, quickly took control and Kulusevski, who played for Parma last season, was given too much space in the penalty area and steered the ball in from Alex Sandro's pass in the 23rd minute.
Ronaldo added the second with a towering header three minutes later and Juve were on their way.
Leonardo Bonucci missed a third from close range just before halftime but it did not matter as Ronaldo scored with an angled drive three minutes after the break.
Morata was rewarded for an excellent performance with the fourth as he headed in from Federico Bernardeschi's cross late in the game.