Ronaldo struck with a fine free-kick in the second minute before heading a second after 69 minutes.
Gonzalo Higuain scored a third as Jose Mourinho's side closed the gap to leaders Barcelona back up to 13 points after their great rivals had earlier won 3-0 away to Real Zaragoza. Defeat left Bilbao eight points above the relegation zone.
Real Madrid took the lead in only the second minute and it came from a familiar source.
Ronaldo scored his 30th league goal of the season and 49th in total with a curling free-kick from 30 yards which gave Gorka Iraizoz no chance in the Bilbao goal.
Ronaldo had been fouled by Ander Herrera in Real's first attacking move of the game and he got up to curl the ball into the top left corner of the goal.
It took five minutes for Bilbao to threaten the Real goal but Gomez Ibai was ruled offside in the move.
Ronaldo tried another shot from distance but this time was off target and Di Maria also failed to work Iraizoz as Real could not build on their early opening.
Bilbao clearly opted to rough up their opponents and continued to give away free-kicks in a bid to stem Real's charge towards goal.
The home side finally get an effort on target when Luka Modric was booked for handling the ball but Ibai hit the free-kick straight at the defensive wall.
With 20 minutes gone Bilbao's Markel Susaeta hit a shot from the edge of the area which Diego Lopez tipped around the post.
With 10 minutes left in the first half Sami Khedira shot from 20 yards but the save was comfortable for Iraizoz in the Bilbao goal.
Ibai was again off target with the first shot of the second half before Karim Benzema saw Iraizoz keep out his effort as Real pressed once more.
Iker Muniain and Ibai were both wide with long shots as Bilbao did their best to force their way back into the game before Ronaldo tried a lob which went over the bar.
Real strengthened their lead after 69 minutes following a foul by Mikel San Jose on Jose Maria Callejon.
Xabi Alonso's free-kick was met with a Ronaldo header as the forward netted for the second time in the game.
With 15 minutes to go Ronaldo became provider when his pass set up Higuain who shot into the bottom corner of the goal to extend the visitors' lead.
Bilbao did their best to grab a consolation but Gaizka Toquero's cross was cleared by Sergio Ramos and Iturraspe shot over the bar as Real comfortably claimed three points.