The Portugal international has now scored 13 goals in six league appearances this season and his latest exploits saw him draw level with Alfredo Di Stefano and Telmo Zarra with 22 trebles in the Spanish top flight.
Gareth Bale set up the opening two of Ronaldo's strikes on Sunday, with the third coming in the closing minutes, although the ball appeared to come off his elbow on its way in.
Karim Benzema was also on the scoresheet at the Santiago Bernabeu with two goals nestled in between Ronaldo's strikes.
The win moves Real into fourth place in the table and piles more misery on Ernesto Valverde, the Bilbao head coach having seen his side's winless run extended to five league games.
Earlier in the day, Sevilla climbed into third place with a convincing 4-1 victory over strugglers Deportivo La Coruna, who remain bottom.
Stephane M'Bia's 24th-minute strike opened the scoring for Unai Emery's side at the Estadio Ramon Sanchez Pizjuan, but Haris Medunjanin levelled a minute after the half hour.
Carlos Bacca restored Sevilla's lead before the break with M'Bia and Vitolo completing the win, while Bacca also missed a 68th-minute penalty.
Villarreal got back to winning ways in the league on their trip to Celta Vigo, as two goals from Moi Gomez and one from Mario Gaspar sealed a 3-1 victory.
Gomez netted twice in a minute during the first half but Villarreal were denied a two-goal advantage going into half-time as Joaquin Larrivey pulled one back.
Celta, who suffered their first loss of the campaign, were reduced to 10 men in the 86th minute when Andreu Fontas was shown a second yellow card, and their day got even worse as Gaspar sealed Villarreal's win.
Meanwhile, Espanyol climbed into the top half with a 2-0 win over Real Sociedad.
Goals from Lucas Vazquez and Cristhian Stuani wrapped up all three points for Sergio Gonazalez's side and left Sociedad without a league win since August.
