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Simeone's side battled to a 1-0 victory over rival Real Madrid on Monday (AEST), and was soon ahead at Estadio Martinez Valero when Matheus Cunha opened the scoring in the first half.
Rodrigo de Paul added a second after the interval and Elche rarely threatened Jan Oblak's goal in response, failing to have a shot on target all game.
It mattered little for the boisterous home crowd as Real Mallorca's stalemate at Sevilla on Thursday (AEST) confirmed safety for Elche, while Atletico climbed into third – six points clear of fifth-placed Real Betis with two games to go.
Sime Vrsaljko was forced off with injury after just six minutes before Cunha curled a presentable opportunity over in the opening exchanges.
Elche had scored two of their last three league goals from set-pieces and both Lucas Boye and Pedro Bigas headed narrowly off target from corners, but Atleti struck first.
Cunha opened the scoring after 28 minutes when substitute Renan Lodi latched onto Antonio Griezmann's lofted pass to drill across for the Brazil forward to poke home.
Elche fans were in celebratory mood after the interval as news filtered through of Mallorca's stalemate with Sevilla, while Bigas had to clear off the line as Cunha's deflected strike looped goalward.
A slick passing move resulted in Atletico doubling their lead and sealing victory, with De Paul exchanging a quick one-two with Griezmann, who unselfishly squared for the midfielder to tap-in.
Substitute Luis Suarez was denied his 12th goal of the LaLiga season by the offside flag in stoppage time, as Atleti cruised to victory.