Los Granotes stun the Europa League semi-finalists to keep their Champions League aspirations alive, while Simeone's side are now six points adrift of fourth
Levante moved into fourth place and level on points with Valencia after a 2-0 victory in Liga against 10-man Atletico Madrid at Ciutat de Valencia.
The home side took the lead in the first minute through a Valdo header, and Arouna Kone doubled their lead with another header eight minutes later to kill the game early on. Atletico's misery was complete in the 83rd minute when Miranda received his marching orders for a second yellow card.
Barely had the match got underway and the hosts were in front. In the first minute Jose Barkero delivered an accurate cross from the left towards Valdo in the middle of the penalty area and the attacker's glancing header bounced in off the right-hand post.
Their dream start got even better when Barkero was the provider once again with a free-kick on the right of the box. He whipped the ball into the danger area with his left foot and Arouna Kone’s header diverted the ball into the net past the reach of Thibaut Courtois.
Los Rojiblancos were left stunned by early events, especially after coming into the game on three successive victories. Gabi had a tame effort straight at Gustavo Munua, and Eduardo Salvio's shot was deflected behind after a scramble in the box from a corner.
Atletico were on top but the hosts were looking increasingly dangerous on the counterattack. Before the half-hour, the home support expressed their delight, as Valdo showed skill and pace to beat his man down the right-hand side, but his pass into the box was smashed high and wide by Barkero.
Diego Simeone’s side came out the stronger of the two teams in the second-half. Arda Turan had a snap-shot at goal from the edge of the area, but Munua parried. From the resulting corner, Joao Miranda had an effort on goal, yet the keeper was equal to it once more. The visitors were clearly missing the clinical finishing of Radamel Falcao, who has scored eight goals in his last eight games.
With half an hour left and the visitors desperately searching for a goal, Diego had an effort with 30 minutes remaining, which rolled harmlessly into the hands of Munua.
Five minutes later Simeone brought on Falcao for Salvio in a hope to salvage something from the match. He instantly got into the action, getting to the ball before Munua, but heading wide. Then the Colombian was close to scoring soon after, his header going wide of the left-hand post.
The result was in no doubt a few minutes later though, as Atletico defender Miranda was sent off for a second bookable offence, tugging back a Levante player after he had been cautioned for a dangerous tackle ten minutes before.
The visitors were still plugging away though. With minutes left, Diego’s free-kick was chipped into the box, and Falcao’s header was acrobatically saved by Munua.
Juan Ignacio Martínez’s team temporarily move into fourth place. The loss for Atletico means they are six games without victory away from home in the league; their away form restricting their chances of reaching fourth position.