The Portuguese former World Player of the Year smashed in a trademark swerving free-kick in the 22nd minute at the Madrigal and followed up with a similar effort in second-half stoppage time to complete a 3-1 victory.
His second of the night equalled the record jointly held by former Real striker Hugo Sanchez (1989/90) and former Athletic Bilbao forward Telmo Zarraonandia, known as Zarra (1950/51).
"The run I am on is good, not for me but for the team, because scoring so many goals is very good for everyone," Ronaldo, who has netted nine goals in his last three matches, said.
"I am pleased on a personal level, although not completely because we wanted to win the league and the Champions League," the 26-year-old former Manchester United player added.
Ronaldo has scored 51 in all competitions this season, including six in the Champions League and seven in the Copa del Rey, and can set a league record with a goal in Real's final match of the season at home to Almeria next weekend.