Ahead of the game, both sides were looking to arrest their slumps in form. In what was billed as a tight, low-scoring affair, individual errors proved costly for the visitors as Villarreal romped home to leapfrog Atleti into fourth place.
Villarreal applied the early pressure, with Roberto Soriano threatening Oblak's goal from distance, but despite the home side's dominance it was the Rojiblanco who came closest to breaking the deadlock, Koke hitting the post from a corner.
The opener came when Villarreal took advantage of some uncharacteristically sloppy defending by the visitors. A loose back-pass from Tiago was intercepted by Pato and fed into the path of Manu Trigueros. The in-form midfielder took it in his stride and hit a composed finish into the bottom corner for his third league goal of the campaign.
The guilty Tiago was immediately hauled off by Simeone and replaced by Saul Niguez.
Villarreal almost let the lead slip a minute later when Griezmann broke free down the right and saw his low shot bounce under the sprawling Asenjo and wide of the far post.
Jonathan dos Santos doubled the home side's lead, pouncing on Pato's spilled cross to slot home at the second attempt. To make matters worse for Atleti, goalkeeper Jan Oblak injured himself in the process and was forced off with a suspected shoulder injury.
Atleti never recovered from those two first half goals and Roberto Soriano capped off the win deep into stoppage time. This win for the Yellow Submarine delivers a crushing blow to Atlético's title hopes, as they drop into sixth, and will do little to quell speculation over Simeone's future at the club.
Meanwhile, his opposite number Fran Escriba expressed pride for his side's performance on Villarreal's official site:
"I've always believed in this team and I think we have proved a great team against Atletico.
"The European qualification has helped us gain confidence. I knew we could win. We were very much involved. With this level of self-commitment the team will always be closer to winning. "
"We did not make mistakes and we did a lot of things well. I've seen the team with a lot of game control. In the second half we managed to ensure that nothing happened in our area. We were very tidy and limited the opposition."
Villarreal (4-4-2): Asenjo; Mario, Alvaro, Ruiz, J. Costa; J. dos Santos, Bruno, Trigueros (N'Diaye 90+2'), Soriano; Pato (Rodrigo 79'), Sansone (Santos Borre 89')
Subs not used: Fernandez, J.Angel, Suarez, Poveda
Goals: Trigueros 28', J. dos Santos 38', R. Soriano 90+3'
Bookings: Sansone 42', J. dos Santos 45+2', Alvaro 85'
Atlético Madrid (4-4-2): Oblak (Moya 40'); Juanfran, Savic, Godin, Lucas; Correa (Carrasco 65'), Tiago (Saul 29'), Gabi, Koke; Gameiro, Griezmann
Subs not used: Vrsaljko, Gaitan, Gimenez, Torres
Bookings: Correa 45', Gabi 67', Saul 85'