Madrid had played 15 previous home games against Alaves in LaLiga, winning 14 of those. They lost the other game, a 1-0 setback in May 2000, but the Santiago Bernabeu was a fortress that Alaves had found hard to crack.
With Madrid in their temporary home of the Alfredo di Stefano stadium this season, it was a completely different story. Despite Casemiro grabbing a late consolation, coach Zidane was left to pick up the pieces from a worrying performance.
Alaves were handed a fifth-minute penalty when Victor Laguardia's header struck Nacho on the upper arm, and Perez found the left corner with a confident strike from the spot.
Madrid keeper Thibaut Courtois then prevented a second goal, producing a sharp stop to palm away a chip from Perez who got in behind the Madrid defence.
A hobbling Hazard, meanwhile, had to be substituted just before the half-hour mark, his wretched run of luck continuing. Moments earlier he had taken a fall in the Alaves penalty area.
Toni Kroos was denied by a fine double save from Fernando Pacheco, after a shambolic attempt by Alaves to walk the ball out of defence from a goal kick.
But Madrid were counting the cost of Kroos missing out as Alaves stretched their lead in the 49th minute. Courtois tried to pick a pass to Casemiro, but it was never on and Joselu stole in to intercept and side-foot into the empty net from 25 yards.
Perez was denied by Courtois as the former Deportivo La Coruna and Arsenal striker again breached the home backline, before Joselu then sent a thumping drive just wide of the top left corner as the two goalscorers combined.
Shots from Rodrygo and Lucas Vazquez went narrowly wide as Madrid sought a way back into the game. Casemiro netted from close range after 86 minutes but they could not force a late leveller, Isco going close when he clipped the top of the crossbar in the sixth minute of additional time.