Lucas Perez and Joselu pounced on a Thibaut Courtois howler as Madrid suffered a third defeat in its opening 10 LaLiga games this season, Los Blacos' title defence getting off to a rocky start.
Madrid had played 15 previous home games against Alaves in LaLiga, winning all 14 of them. It lost the other game – a 1-0 setback in May 2000 – but Santiago Bernabeu was a fortress that Alaves had found hard to crack.
With Madrid in its 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 was 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 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 was counting the cost of Kroos missing out as Alaves stretched its lead in the 49th minute. Courtois tried to pass to Casemiro, but it was never on and Joselu stole in to intercept and fire 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 goal scorers 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 the hosts could not force a late leveller, Isco going close when he clipped the top of the crossbar in the sixth minute of stoppage-time.