Despite dominating the first period, Madrid led by just the one goal at the interval with Ronaldo finding the back of the net after 21 minutes.
The Portuguese had his second after 66 minutes, before Di Maria got in on the act with a late double as the Spanish outfit moved onto six points in Group B.
Here Sports Mole dissects the 90 minutes of action between the two European rivals.
On target: 7
On target: 3
Was the result fair?
On the balance of play, it is difficult to argue that Madrid did not deserve to record a comfortable three points this evening. Despite taking a one-goal lead into the interval, they did struggle in the final third in the opening half, with the final pass too often failing to reach its desired destination. That changed in the second, but the four-goal score is slightly harsh on Copenhagen, who defended well for long spells in the Spanish capital.
Real Madrid's performance
Madrid needed a big performance following their 1-0 loss to Atletico Madrid at the weekend and up until the 66th minute, it appeared that the team were moving towards a fairly lacklustre 1-0 win, which would not have pleased the home supporters. However, the goals came in the latter stages with Ronaldo completing his brace before Di Maria added two more. The Spanish outfit have been far from watertight in defence this season, but they managed a clean sheet this evening, which is certainly a positive.
The Danish outfit entered the match in a poor run of form domestically, but they did knock the ball around with confidence in the early stages. That said, they never really threatened Iker Casillas in the Madrid goal until the final few moments. They would have accepted a one or two-goal defeat, but their goal difference took a hit in the final 20 minutes. However, their push for the knockout stages of the competition will be built on home form, rather than at places such as the Bernabeu.
Sports Mole's man of the match
Angel di Maria: The Argentine had a number of chances in the first period, but poor finishing cost him the chance to open his tally. However, he responded in the second half with two strikes to add gloss to the scoreline. The winger had been widely linked with a move away from Madrid in the summer, but he was extremely influential this evening.
In fairness to Copenhagen goalkeeper Johan Wiland, he made some good saves this evening. However, he had a horror after 21 minutes when he came and got nowhere near a Marcelo cross, leaving Ronaldo with a simple header from close range. The goal came at the perfect time for the home side, who had struggled for inspiration in the early stages.
Neither manager will have had too many complaints about the performance of Matej Jug this evening. The Slovenian was hardly seen in the first period as he issued just the single yellow card, while he also allowed the match to flow in the second 45 minutes. It was a fairly straightforward evening for the official.
Real Madrid: Carlo Ancelotti's side will attempt to get back on track in La Liga when they travel to Levante at the weekend.
Copenhagen: The Danish outfit also return to domestic duty this weekend with a home clash against Sonderjysk Elitesport.