Ronaldo, banned for pushing a referee after being sent off in the first leg of the Spanish Super Cup, opened the scoring after just 12 minutes from Gareth Bale's low cross.
The Portuguese doubled his tally from the penalty spot before Sergio Ramos's overhead kick rounded off the scoring. Real move to the top of Group H alongside Tottenham Hotspur, who ended their Wembley hoodoo with an impressive 3-1 win over Borussia Dortmund. Ronaldo has now struck 12 times in his last six Champions League games.
"He is the best in the world. We know he will always score goals," said Madrid boss Zinedine Zidane. "With a bit more luck today he could have scored four."
Ronaldo described the length of his ban as "persecution" on the part of the Spanish football federation and his absence has been felt by Real in profligate performances in being held at home by Valencia and Levante.
"We are on a run of games without scoring many goals, but you can't thrash teams all the time," said Ramos. "Cristiano has so many goals in him and we feel it. "Hopefully he stays in form. You can't question the levels he reaches every year."
Zidane admitted that the club's failure to replace Alvaro Morata had left his striking options limited, particularly in the absence of Karim Benzema through a hamstring injury. However, with Bale excelling back on the left, Ronaldo filled that void as he swept home at the back post from the Welshman's cross.
Ronaldo then headed into the side-netting from a similar position from another Bale delivery moments later. Real suffered an injury setback midway through the half as Mateo Kovacic limped off to be replaced by Toni Kroos. And the hosts' rhythm was disrupted as they struggled to create more clear-cut chances against the dogged Cypriot champions before the break.
Ronaldo thought he had doubled his tally a minute into the second half as his volley from Dani Carvajal's pinpoint cross came off the underside of the bar, but didn't cross the line despite his protests.
Madrid's luck turned moments later when Roberto Lago was very harshly penalised for handball from Bale's deflected cross and Ronaldo smashed home the resulting penalty, he showed his hunger for more goals as he retrieved the ball from the net and raced back to the halfway line.
However, it was Ramos who struck next in acrobatic fashion from point-blank range. Ronaldo thought he had bagged an eighth Champions League hat-trick when he swept home Luka Modric's cross. But he was denied by the offside flag as Real had to settle for three as they began their quest for a 13th European Cup.
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