The home side dominated proceedings in the first period, but they lead by just the one goal at the interval following a Cristiano Ronaldo header after 21 minutes.
Ronaldo had his second with 25 minutes remaining, before Angel di Maria completed the scoring with a late double.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
REAL MADRID: Casillas; Carvajal, Pepe, Varane, Marcelo; Modric, Illarramendi, Khedira; Di Maria, Benzema, Ronaldo
COPENHAGEN: Wiland; Sigurdsson, Bengtsson, Mellberg, Jacobsen; Claudemir, Delaney, Gislason; Braaten, Jorgensen, Toutouh