The Portugal star netted his ninth of the group stages after Luka Modric had put the visitors in front as they cruised to the last 16 in style
The Portugal star netted his ninth goal of the group stage after Luka Modric had put los Blancos ahead in the first half as Carlo Ancelotti's side cruised into the last 16.
Real, which had already secured the top spot, finishes with 16 points from its six fixtures, while Copenhagen exits the competition and will also miss out on a Europa League berth.
After a slow opening, Luka Modric sparked the match into life with a superb curling effort, but Carlo Ancelotti's charges survived a scare when Nicolai Jorgensen had an effort ruled out for an apparent handball.
The game was put beyond doubt when Ronaldo notched his record-breaking goal from just outside the six-yard box, and he missed the opportunity to make it 3-0 when having a penalty saved in the closing stages.
Ronaldo was predictably named in Madrid's side following his return to fitness, while Rurik Gislason and Jorgensen came into Copenhagen's starting XI.
Both sides struggled to create chances in a lackluster opening with a Gareth Bale header and Karim Benzema's tame volley the only efforts of note.
However, Modric lit up the tepid affair with a sublime effort in the 25th minute.
The Croatia international received the ball on the right-hand side of the box before turning his marker and curling into the top corner from 20 yards.
The goal appeared to settle Real, which began to display greater fluency.
A speculative volley from Ronaldo bounced in front of Johan Wiland, forcing the goalkeeper into a smart parry.
Despite its dominance, Real looked to have been pegged back shortly before the interval.
Jorgensen rose highest to divert a cross from the right past Iker Casillas, but his effort was chalked off with replays suggesting the striker had handled.
The visitors nearly doubled their lead early in the second half when Ronaldo weaved through the defense only to poke an effort straight at Wiland.
It was not long before the former Manchester United forward did find the back of the net.
Marcelo's deep cross was headed across goal by Pepe, allowing Ronaldo to tap home from close range.
With a two-goal cushion Real was in complete control and it had the ball in the net again on the hour mark when Nacho tapped home, yet his celebrations were curtailed by the offside flag.
Ronaldo came agonisingly close to another goal with 15 minutes remaining when his low left-foot strike rebounded to safety off the inside of the post.
Copenhagen was unable to create a clear-cut opportunity and could have fallen further behind when Bale's header from Marcelo's center flashed wide.
Real then spurned a golden chance to add a third in the 89th minute. Ronaldo was felled in the area by Thomas Delaney, but the former saw his penalty saved by Wiland.