Los Che inflict first Atletico defeat
Roberto Soldado's stunning opener gave the hosts an interval lead and Nelson Valdez rounded off the victory in added time. Costa was dismissed in the 90th minute for a second booking and coach Mauricio Pellegrino and his assistant Carlos Compagnucci were sent from the dugout in separate incidents, but it was Valencia's day nonetheless.
Atletico started the brighter and Gabi Fernandez was first to threaten, shooting over from 12 yards, and Radamel Falcao curled a 14th-minute free-kick high over the bar. They went closer when Arda Turan's header was well saved low down by Diego Alves and Falcao was clearly held by Joao Pereira, preventing him latching onto the rebound.
To add injury to insult, he was caught by Soldado's trailing foot after the striker cleared the loose ball behind and had to go off to have his head bandaged. The breakthrough came at the other end in the 20th minute as Soldado met Adil Rami's long pass, dropping over his shoulder, with a superb volley into the far top corner.
Rami blocked Adrian Lopez's shot and was off target with a hopelessly ambitious effort of his own, while Falcao could not direct the ball goalwards when surrounded by defenders. Valencia coach Mauricio Pellegrino was sent to the stands before half-time for protesting as one of his players lay injured.
Arda flashed an effort just over in an otherwise low-key start to the second period. Atleti introduced Cristian Rodriguez in place of Emre Belozoglu and the newcomer was involved in the build-up as Falcao headed Filipe Luis' cross over.
Tiago Cardoso was booked for jabbing an arm at Adrian and Costa followed after going through the back of Jonas Oliveira. Alves parried away Rodriguez's long-range free-kick but Valencia had the opportunity to finish the game off when Andres Guardado raced into the penalty area and fired over.
Costa collected a harsh second booking, moments after taking over the captaincy from the substituted Soldado, when his arm caught Raul Garcia. The protests from the bench saw assistant coach Compagnucci sent to the stand.
Despite the upheaval, though, Valencia grabbed a second goal deep into added time when Sofiane Feghouli played in Soldado's replacement, Valdez, to round goalkeeper Thibaut Courtois and finish left-footed.