The Portuguese struck early in the second half to take his tally to nine goals in the current Champions League, a mark he previously shared with four other players
Ronaldo, who missed Madrid's 4-1 win over Galatasaray in the last group game, struck with a low finish at the far post to give Madrid a 2-0 lead early in the second half in the Danish capital and now has nine goals in Europe's premier club competition this season.
"All goals are important for the team and it was special to break the record today, but I don't think about records," Ronaldo told his team's official website shortly after the match. "The main goal is to win."
The Portuguese previously shared the record of eight with Hernan Crespo, Ruud van Nistelrooy, Filippo Inzaghi and Zlatan Ibrahimovic, who was left out of Paris Saint-Germain's trip to Benfica on Tuesday.
Ronaldo, who was suspended for Real's Copa del Rey clash at Olimpic Xativa on Saturday, had missed Madrid's last three games after his recent thigh injury but took his season total for the Spanish side to 26 in 19 games on Tuesday. He later saw a penalty saved by Copenhagen goalkeeper Johan Wiland.
Ronaldo said he is still not 100 percent healthy.
"I'm coming back bit by bit. I'm at a good level, but not my best," he said. "I feel good and eager to help the team."
Cristiano struck a hat trick in the 6-1 win over Galatasaray, hit three in two games against Juventus and netted three in the two meetings with Copenhagen.
His goal on Tuesday was Madrid's 800th in European Cup football.