Carlo Ancelotti's men have topped Group B by some distance and finish with 16 points from 18 after a record-breaking night.
Luka Modric's fine opener was the 31st successive European game in which they have scored, setting a new competition record, before Ronaldo made it safe after the break.
The Ballon D'Or winner-in-the-making had a chance to make it two late on from the spot but those in the Danish capital were stunned as the normally-faultless frontman's effort was saved.
The loss, although expected, leaves Copenhagen out of both the Champions League and Europa League, even before Galatasaray and Juventus replay their abandoned game.
It had been rumoured that Madrid would allow Ronaldo to start on the bench with top spot already in the bag, but his appearance in the starting line-up came as no surprise either.
What did cause some shock, though, was that it was Copenhagen who started on the front foot.
Piette Bengtsson mishit wide after a fine counter, before Christian Bolanos drilled a shot into Nacho.
Madrid came into things after that and Karim Benzema drew a save from Johan Wiland, before the same men tangled again to the same result.
The pressure continued to build and with 25 minutes on the clock Modric scored, turning outside the area, fading and then curling in a brilliant right-footer.
Ronaldo was keen to get in on the act but found Wiland in the way of a similar effort, before being denied by the impressive stopper again.
Gareth Bale was also frustrated by Wiland, as was Xabi Alonso as the traffic became one-way.
The interval did little to stop that and Wiland produced a fine near-post stop to thwart Ronaldo again, but the Portuguese got his reward in the 48th minute.
Marcelo's deep cross was nodded down by Pepe and Ronaldo did the rest for Real's 800th goal in European football.
An 801st nearly followed but Nacho was called offside as he tapped in, before the home side remembered how to attack as Igor Vetokele shot over from close range.
Ronaldo typically showed greater accuracy at the other end, although only against the post after a smart run, before letting himself down when he drilled at Wiland from 12 yards after he had been chopped down by Thomas Delaney.