Unai Simón was called into action twice moments apart to deny Mbappé and Vinícius Júnior after unconvincing defending from his teammates in the opening stages.
However, there was nothing the goalkeeper could do to stop Mbappé in the seventh minute, as the Frenchman collected Trent Alexander-Arnold’s pass, glided away from Iñigo Lekue, cut inside Aymeric Laporte and smashed the ball past Simón.
Gorka Guruzeta blazed his attempt over from a Nico Williams cross as the hosts searched for a response, but Mbappé and Vinícius Júnior continued to pose a threat going the other way.
Guruzeta then saw a venomous attempt stopped by Thibaut Courtois, who also spread himself superbly to deny Álex Berenguer on the half-hour mark. Vinícius Júnior was released behind Ernesto Valverde’s backline twice shortly after but hit the post from a tight angle and was then stopped by Simón.
Los Blancos still got their second before the break, as Alexander-Arnold’s cross was headed back across goal by Mbappé for Eduardo Camavinga to nod home.
Valverde responded with a double change ahead of the restart, and while Mbappé hit an attempt within 30 seconds, it wasn’t much longer until Courtois had to tip over an ambitious Mikel Jauregizar with the hosts refusing to give up.
Despite the goalkeeper’s work, there was a blow for Los Blancos as Alexander-Arnold went off injured in the 55th minute.
There was then a coming together between the two teams after an incident involving Mbappé and Adama Boiro, but the Frenchman clearly wasn’t bothered as he fired an audacious shot from range past Simón shortly after.
Camavinga also had to go off injured despite trying to carry on after a challenge from Berenguer, but Guruzeta couldn’t find the target with his late attempts as Real Madrid convincingly ended a run of three consecutive draws in LaLiga to ensure they remain just one point behind the leaders Barcelona.
They also inflicted a fourth defeat on Athletic Club in their last six league matches, leaving the hosts eighth for now.
Flashscore Man of the Match: Kylian Mbappé (Real Madrid)