Luka Modric had given a surprisingly strong Madrid side the lead with a wonder strike on 25 minutes.
Ronaldo then doubled the advantage just after the break with a clinical finish from close range, but it wasn't a perfect night for the Portuguese as he had a late penalty saved by Copenhagen keeper Johan Wiland.
Real's two goals also meant they equalled a competition record of 20 goals in the group stages as they finished with 16 points from a possible 18.
Ronaldo was making his return to the side after three games out through injury and suspension respectively, whilst Gareth Bale also started after missing Saturday's 0-0 draw away to minnows Olimpic Xativa in the Copa del Rey due to flu.
On a freezing night and on a pitch in awful condition in the Danish capital it was perhaps unsurprising that the hosts made the more forceful start.
However, they failed to seriously trouble Iker Casillas and Madrid began to threaten midway through the half.
Karim Benzema was first to have an effort on goal as his low drive was well-handled by Wiland in the Copenhagen goal.
Just three minutes later though, the keeper was left helpless as Modric curled in his first goal of the season with a stunning strike from 25 yards.
Wiland then had to be alive to deny Ronaldo as he bundled the Portuguese's effort round the post.
Copenhagen did have the ball in the net before half-time when Thomas Delaney outjumped Casillas. However, the goal was ruled out as the midfielder not only appeared to foul the Spanish captain but also put the ball in the net with his hand.
Ronaldo had to wait just three minutes after the break to make his mark as he latched onto Pepe's well-directed knockdown to fire home from close range.
The former Manchester United man then struck the post with an in-swinging effort as Madrid controlled the second-half with ease.
And he had the perfect opportunity to double his tally for the evening when he was felled inside the area by Delaney.
But Wiland stood up well to divert his dinked effort behind for a corner and moments later Bale failed to connect from barely three yards out with the goal at his mercy to keep the score down.