Defying their underdog status, the hosts could have taken the lead inside just two minutes, as David Torres’ close-range header from a corner was well-saved by Thibaut Courtois.
The goalkeeper was also on hand to tip Mamadou Sylla’s strike wide, before Antonio Rüdiger tried his luck from distance at the other end. Karl Hein parried the ball away for a corner, which resulted in Aurélien Tchouaméni heading onto the roof of the net.
It took Los Blancos to the half-hour mark to find the breakthrough, as the in-form Mbappé curled into the far corner after playing a lovely one-two with Jude Bellingham, giving the visitors a narrow half-time lead.
Carlo Ancelotti’s men took control in the second half as Mbappé netted his brace - and seventh goal in five matches - before the hour-mark. The Frenchman collected Rodrygo’s pass before beautifully placing the ball into the bottom corner to put the result beyond doubt.
The visitors kept the ball well after that and were patient with their chances, with one particular passing move almost resulting in a third goal from substitute Luka Modrić, who just struck past the far post.
As the 90-minute mark approached, Madrid were awarded a penalty to make it three, with culprit Mario Martín shown a second yellow card and duly sent off against his parent club. Mbappé stepped up and made no mistake, sending Hein the wrong way to score his first hat-trick for Los Blancos.
Los Blancos have now lost just once in 26 away matches and sit in pole position to defend their title, while a third successive defeat for Valladolid leaves them at the foot of the table and five points adrift of safety.