Madrid, under pressure following a poor domestic run and without the injured Gareth Bale, completely dominated the Danish champions at the Santiago Bernabeu Stadium and now leads Group B with six points.
Madrid coach Carlo Ancelotti said he was pleased with the match, saying it had a good beginning, intensity and balance. "We tried to carry on scoring right into the last minutes, there was a good attitude in the team."
Even Copenhagen coach Stale Solbakken praised Ronaldo, calling him a match-winner. "He is the man of the match with his two goals."
Juventus drew 2-2 against Galatasaray in the other group match on Wednesday and is in second spot with two points.
Madrid took the game to their Danish opponents from the start, with Karim Benzema heading wide with only goalkeeper Johan Wiland to beat.
But the hosts were rewarded for constant pressure when Marcelo's cross dipped over the outstretched arms of Wiland to find Ronaldo at the far post for the opening goal.
Both Benzema and Di Maria had glaring misses in the first half as Di Maria's pace and verve opened up space in the attack and Marcelo continued to provide pin-point crosses.
Copenhagen needed 28 minutes to test Madrid goalkeeper Iker Casillas, who played his first full game of the season after injuring his hand in the win over Galatasaray.
Rurik Gislason headed a 40th-minute corner past Casillas but Luka Modric cleared it off the line not before Copenhagen coach Stale Solbakken did a cartwheel along the sidelines thinking his side's best opportunity of the period had gone in.
Benzema's deft backheel pass found Di Maria's run into the box, leading to a short cross that Ronaldo headed home for his 55th goal in the competition on his 100th appearance in the Champions League.
After holding Juventus to a draw at home in the last round, Copenhagen was outplayed in the Spanish capital and had little chance of a comeback after Di Maria cut inside to unleash a left-foot shot beyond the diving Wiland.
The Argentina forward found similar space in added time, when Casillas made a pair of saves to keep a clean sheet.
Ancelotti said the club was not worried about Bale's injury. "He's had a scan and has nothing special. He has to recover his condition because his pre-season wasn't so good."