The Portuguese struck in the second half against Copenhagen to take his tally to nine goals in the current Champions League, a mark he previously shared with four others 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.
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.
The 28-year-old struck a hat-trick in the 6-1 with Galatasaray, hit three in two games against Juventus and now has three in the two meetings with Copenhagen.
His goal on Tuesday was Madrid's 800th in European Cup football.