Both sides had opportunities in an open first period, but Luka Modric's curling effort left Madrid with a one-goal lead at the interval.
It was 2-0 in the early stages of the half when Cristiano Ronaldo converted from close range, but the Portuguese passed up the chance to make it three in the latter stages when he missed from the penalty spot.
Here, Sports Mole dissects the 90 minutes of action between the two Group B rivals.
On target: 6
On target: 12
Was the result fair?
In truth, Madrid should have won by more than two goals in Denmark this evening. The home side had their moments during an entertaining European contest, but they never really looked capable of turning it around after Modric opened the scoring. The Spanish outfit dominated in the second period and should have made it more comprehensive in the latter stages, but Ronaldo and Gareth Bale both passed up golden opportunities.
As expected, the home side were full of running and intensity in the opening 20 minutes, but they struggled to recover after Modric sent Madrid into the lead. It was a similar story in the second period, with their early initiative fading after Ronaldo put the away side two goals ahead. They can take heart from their defensive performance, however, especially in the second half as Madrid upped the tempo. There are plenty of teams that would have been beaten by four or five with the Spanish side in this type of form.
Real Madrid's performance
Carlo Ancelotti's side demonstrated why they are one of the favourites to lift the Champions League this season. On a bumpy pitch, the La Liga side controlled the entire tempo of the match, while they were much improved in defensive areas. There is no doubt that Xabi Alonso brings a calmness to their midfield, with the Spaniard excellent alongside Modric in the middle of the park. It should have been more comfortable in terms of the scoreline, but it was a slick, composed performance from Los Blancos.
Sports Mole's man of the match
Luka Modric: It took the Croatian a little bit of time to make his mark in Spain, but he is now a key member of Madrid's first XI. The former Tottenham Hotspur midfielder was different class this evening as he bent one into the top corner in the first half, in addition to controlling the whole tempo of the game. However, he was forced off late on with an injury.
Ronaldo should have completed his brace in the latter stages when presented with a penalty, but the Portuguese fired his spot kick straight at Johan Wiland. Had Ronaldo scored, Madrid would have set a new record for most goals scored in a group stage of a Champions League campaign (21). As a result, they join Manchester United and Barcelona on 20.
Felix Brych had a fairly comfortable night in Denmark. The 38-year-old got the major decision correct in the first period when he disallowed Copenhagen an equaliser when Thomas Delaney handled into the back of the net in a challenge with Iker Casillas. A number of late challenges occurred throughout the 90 minutes, but the official was prepared to analyse each situation before entering his pocket.
Copenhagen: Copenhagen will attempt to continue their strong run of form in their domestic league when they travel to AGF on Sunday.
Real Madrid: The Spanish outfit also return to league action at the weekend with a trip to lowly Osasuna.