The win continues their 100 per cent start to the season, while all eyes at the club now turn to the potential arrival of Gareth Bale later on Sunday.
Former Malaga star Isco was in electric form for Los Blancos, taking his tally to four goals in three Liga games. Cristiano Ronaldo netted either side of those strikes to make it 202 goals in 202 games for the Spanish club and take his career tally to 365 goals, while Ibai Gomez scored a consolation.
The midday kick-off in Madrid perhaps was the main factor in a sluggish start to the match, with glimpses of energy from Bilbao winger Markel Susaeta.
Ronaldo took about 23 minutes to dust off the cobwebs, making a driving run from the left-hand side towards goal and smashing a right-foot shot into the side-netting.
The following corner-kick – with Iago Herrerin having just gotten a fingertip on to that shot – was headed across goal by Sergio Ramos, but Pepe missed the ball at the near post.
Within a few seconds, Real Madrid opened the scoring through midfield magician Isco, who cushioned a pass from Ronaldo and drove the ball into the net.
Ronaldo and Karim Benzema clashed inside the box as the pair went for a header from Angel di Maria’s inswinging left-footed cross, with the ball striking the Frenchman and flying over the crossbar.
After comparisons with Dixie Dean, Sandor Kocsis, Bob Latchford, Santillana and Jared Borgetti in this morning’s AS newspaper, Ronaldo delivered a crushing blow to Bilbao with a glancing header home from the penalty spot - from a Di Maria set-piece - on the stroke of half-time.
A double switch from Ernesto Valverde – a former coach of Real Madrid – helped Bilbao’s cause, with Erik Moran and Oscar de Marcos adding freshness to the midfield.
The star of the show was former Spurs midfielder Luka Modric, who received a rapturous ovation from the home fans midway through the second period.
The Croatian was tireless in his midfield energy, winning the ball back with ease and hammering the critics from Marca who called him the worst signing of last season.
The Bernabeu cheered “Modric, Modric” as the midfielder sprinted back to his own corner flag to sweep up a potentially dangerous Athletic Bilbao counter-attack.
Real Madrid’s 72,000-strong audience have another hero in their ranks: Isco.
The attacking midfielder danced past Bilbao’s defence at times, with the 23-year-old popping up on 73 minutes to rattle the ball past Herrerin from the edge of the box for his second of the game.
Five minutes later, Valverde’s side finally added an end product to a counter-attack with De Marcos picking out Gomez at the far post.
Carlo Ancleotti was afforded the luxury of introducing Casemiro, Dani Carvajal and Jese into the game as Real Madrid continued their perfect start to the season.
Los Merengues are joint-top on nine points with the impressive Villarreal after three matches.
Now for Bale.