The Portugal international had trained alone in the build-up to the match due to the problem suffered in Wednesday's Champions League victory over Ludogorets, but he showed no ill effects to take his tally to 13 goals in six La Liga games so far this season.
It took just two minutes for Ronaldo to open the scoring with a close-range header and, after Karim Benzema had converted for the second, the FIFA Ballon d'Or winner was again on hand to finish off a crisp attacking move early in the second half.
Ronaldo was at the heart of Real's fourth goal, too, as he selflessly rolled the ball into the path of Benzema to give the Frenchman a second of the match on 69 minutes.
But, predictably, there was only ever likely to be one man who stole the headlines as Ronaldo scored his third - albeit controversially with the aid of his arm - in the 89th minute to add to treble against Deportivo La Coruna and a four-goal haul in a rout of Elche, all in just over a fortnight.
In netting his 22nd Liga hat-trick, Ronaldo also equalled the Spanish top-flight record held jointly by Telmo Zarra and Alfredo Di Stefano.
Real's fourth successive league win lifts them up to fourth in the table, while Bilbao's winless run was extended to seven games in all competitions as pressure begins to build on coach Ernesto Valverde.
The Basque club have not won a competitive game since the end of August and remain in the bottom three after this defeat.
Both sides made a handful of changes from their UEFA Champions League exploits in midweek, with the hosts welcoming Pepe back to the heart of their defence in place of Raphael Varane.
Bilbao, who were beaten by BATE on Tuesday, found themselves behind before they could settle into any sort of rhythm as Ronaldo opened the scoring in just the second minute.
Gareth Bale lifted a cross to the back post from the edge of the penalty area for the Portugal international to register his 11th league goal of the season with a powerful header.
Madrid's pace in attack continued to cause Bilbao plenty of problems and Ronaldo saw a low shot well saved by Gorka Iraizoz prior to Benzema failing to convert two good crosses from Bale.
Having spent the opening 20 minutes chasing shadows, the visitors slowly began to settle into the game, but only Iker Muniain's 23rd-minute strike tested Iker Casillas, the goalkeeper easily tipping over a dipping effort.
Madrid continued to pose the greater threat and, after Ronaldo had seen another chance well saved by Iraizoz, they doubled their lead through Benzema, the striker rising to meet a right-wing corner with a powerful downward header.
Four minutes after the break, Bale was presented a chance to extend their lead even further but the 25-year-old, under pressure from Aymeric Laporte, blazed over at the end of a flowing Madrid move.
They did not have to wait long for the third goal, though, as Bale was released by Benzema before laying the ball on for Ronaldo to tap home his second.
The visitors were barely seeing anything of the ball and with 20 minutes to play they were further behind as Ronaldo raced clear before rolling a pass to Benzema, who applied the simplest of finishes.
Iraizoz's goal remained under threat despite Real's big lead and the goalkeeper made good saves from Ronaldo and Bale in the closing minutes.
Ronaldo's attempts to get his hat-trick saw Iraizoz punch clear a free-kick in the closing minutes but the attacker's moment finally arrived when he deflected a Pepe shot into the back of the net with a minute to go, although replays showed the ball may have come off his elbow.