Following his hat-trick in the 6-1 thrashing of Galatasaray in matchday one, Ronaldo now has five goals in just two Champions League games this season.
The Portuguese headed home the opener midway through the first-half from Marcelo's fine cross and made the game safe 25 minutes from time with another headed effort from Di Maria's cross.
The Argentine winger made it 3-0 himself with a sensational curling effort from 25 yards and rounded off the scoring in stoppage time with another precise left-footed finish.
With Gareth Bale sidelined due to a thigh strain, Real boss Carlo Ancelotti had reacted to Saturday's 1-0 derby defeat to Atletico Madrid by making five changes.
Iker Casillas returned in goal for the first time in nearly nine months at the Bernabeu, whilst Raphael Varane and Marcelo also made their first appearances since recovering from injury.
Madrid didn't have things quite as easy as might have been expected in the early stages with Karim Benzema's header from close range that drifted wide their only clear-cut opportunity.
However, they did eventually make the breakthrough on 21 minutes as Copenhagen keeper Johan Wiland got caught under Marcelo's out-swinging cross from the left and Ronaldo was left with a simple header at the back post.
Di Maria should have made it 2-0 moments later when he side-footed wide from Benzema's intelligent cut-back and then saw a flicked header from another dangerous Marcelo cross creep just wide.
However, the Danish champions were left aggrieved just before half-time when Nicolai Jorgensen's header came back off the bar and the ball brushed Luka Modric's hand as he cleared the rebound off the line.
"It was a very decisive moment at the end of the first-half when it may be given a penalty and he may also have to give a red card as it is a goalscoring opportunity," said Copenhagen boss Stale Solbakken.
"It looks like a penalty for me, but I wouldn't blame the referee as it went very fast."
Madrid continued to dictate play at the start of the second-half without much penetration as Modric fired just wide before a Ronaldo free-kick dropped onto the roof of the net.
The second goal did finally arrive when neat play between Di Maria and Benzema released the former to send over a wonderful cross that Ronaldo bulleted home.
Di Maria sealed a fine individual performance with a sweet left-footed strike six minutes later.
And he piled more misery on Copenhagen in stoppage time as he collected a loose ball inside the area and fired low into the bottom corner.