Goncalo Guedes scored the opener at Mestalla on Wednesday, with Valencia moving within a point of the Champions League places after extending their unbeaten run to 17 games in all competitions.
Madrid, having needed a late Karim Benzema goal to beat bottom side Huesca last time out, underwhelmed again despite the return of star names including Ballon d'Or winner Luka Modric.
Ezequiel Garay superbly converted a corner from Daniel Parejo to double the lead, though Valencia missed out on a sixth straight clean sheet at home in the league due to Benzema's 93rd-minute header.
Sergio Ramos saw an early penalty appeal rejected by referee Santiago Jaime Latre after he was challenged in the air by Garay.
Neto easily claimed a speculative long-ranger from Toni Kroos but Valencia took the lead in the 35th minute after Keylor Navas flapped at a corner.
Guedes and Carlos Soler played a clever one-two and the former beat Navas at his near post with a smart strike.
Soler should have set up Guedes again at the end of a rapid counter-attack started by Neto in the 53rd minute, but instead saw his shot blocked by Navas, while Rodrigo Moreno fired wide.
Zidane introduced Isco and Gareth Bale in a double change but Madrid continued to toil; Marcelo blazed a hopeful volley well over the crossbar and the Brazil left-back was later booked for a blatant dive.
Valencia finally scored the second goal their excellent performance deserved with seven minutes remaining, Garay beating Casemiro in the air to nod home Parejo's terrific corner.
Madrid were denied a late penalty when Ramos was fouled by Mouctar Diakhaby, the centre-back flagged offside after the referee had initially pointed to the spot, although Benzema did get a goal back with just seconds remaining.
What does it mean? Madrid in danger of drifting
With eight games to go, Madrid are a massive 13 points behind leaders Barcelona but 10 points clear of Getafe in fourth, leaving them little to play for. Zidane faces a challenge to keep his side motivated in games that have nothing riding on them.
Valencia, meanwhile, continue their charge and are now surely favourites for the last qualification place for the Champions League,their poor start to the season long forgotten. They are increasingly irresistible at Mestalla.
Parejo runs the game
Capped by Spain for the first time last year, Valencia captain Parejo remains their shining light in the middle of the pitch. His set pieces were a constant threat, a corner setting up Garay for the clincher, and he rarely wasted possession in open play.
Navas keeps goalkeeper debate open
Zidane restored Navas to the starting XI after selecting his son Luca against Huesca, but the Costa Rica international arguably should have done better with the goal.
The Madrid coach has promised to decide on his number one before the 2019-20 season starts but Navas is not making a strong case to be picked over Thibaut Courtois - or the young Zidane.
Key Opta facts
- Valencia are unbeaten in their last 17 games in all competitions (W10 D7), the current best run of any side from the top five European leagues.
- Real Madrid have lost nine of their 30 games in LaLiga this season (W18 D3) - it is their worst total at this stage since 1998-1999 (10).
- Goncalo Guedes has scored three goals in his last five matches for Valencia in all competitions, as many as he had in his previous 52.
- Daniel Parejo has been involved in 12 goals in his 19 LaLiga appearances against Real Madrid - that is more than against any other team (5 goals, 7 assists).
- Karim Benzema has scored 15 goals in LaLiga in seven of his last nine seasons.