Chances were few and far between in the second half, but Isco grabbed his second in the latter stages before Ibai Gomez scored a late consolation for the Basque outfit.
Here, Sports Mole dissects the 90 minutes of action between the two Spanish rivals.
On target: 7
On target: 2
Was the result fair?
On the balance of play, it is difficult to argue that Madrid did not deserve to pick up all three points this afternoon. It took them a while to get going in the first period, but they controlled the latter stages of the half after Isco handed them the lead. Bilbao had their moments, especially in the second half, but they did not do enough to deserve to take something from the game.
It was not vintage Madrid, but it was a professional display from the former Spanish champions. Angel di Maria and Karim Benzema both started despite reported interest from Arsenal, but neither could influence proceedings. Ronaldo also looked slightly off-colour despite his goal, but the midfield duo of Luka Modric and Isco were simply sensational.
Bilbao decided to leave Ander Herrera on the bench this afternoon following interest from Manchester United and there is no question that they missed the Spaniard's presence in the middle of their midfield. They did match Madrid for long periods, while they also enjoyed a lot of the possession for an away side at the Bernabeu. They might have lost, but six points from three games is a respectable return for the club at this stage of the season.
Sports Mole's man of the match
Luka Modric: The Croatian midfielder was criticised for his performances in the early stages of last season, but he is emerging into one of Madrid's key players. He did not feature too heavily as an attacking threat this afternoon, but he was stunning in defensive areas, sniffing out attack after attack, and also used the ball intelligently.
Biggest gaffe of the match
Having already been booked in the first period, Carlos Gurpegi was lucky to remain on the pitch after appearing to elbow Ronaldo in the second half. It would have left his side with 10 men for the final 25 minutes, which would have surely brought a couple more goals for the home team.
Clos Gomez had a successful 90 minutes in the Spanish capital. He was hardly seen in the first period as he allowed the play to flow, but he was called into action to issue a number of bookings in the second half. Despite a positive performance, he should have dismissed Gurpegi for an elbow on Ronaldo in the second period.
Madrid: Carlo Ancelotti's side will attempt to make it four wins from four when they travel to high-flying Villarreal on September 14.
Bilbao: Bilbao, however, must wait until September 16 to continue their domestic campaign at home to Celta Vigo.