Diego Simeone’s side headed into the clash as league leaders, following a brilliant start to the campaign, but a first half goal from Casemiro, and a Jan Oblak own goal, secured the win.
Karim Benzema led the charge in an impressive start at the Estadio Alfredo Di Stefano with Oblak producing a brilliant stop to deny the Frenchman.
However, there was nothing he could do about Casemiro’s opener, as the Brazilian powered home a header from Toni Kroos’ corner.
The visitors did improve after the break, with substitute Thomas Lemar scuffing against the post on 54 minutes, before Carvajal helped to make it 2-0 just after the hour.
The Spaniard’s brilliant 25-yard drive had Oblak beaten, but his effort rebounded back off the post and deflected home off Oblak’s back.
Simeone’s team did look to rouse themselves in the final ten minutes as substitute Saul Niguez forced an instinctive stop from Thibaut Courtois but they could not find a way through.
Image via Real Madrid CF on Twitter