Sevilla opened the scoring after 23 seconds with full back Sergio Escudero punishing lax marking before an Ever Banega penalty and Pablo Sarabia's late strike wrapped up the win.
Antoine Griezmann had got Atletico back into the contest with a stunning long-range right-foot strike after 13 minutes that exposed goalkeeper Sergio Rico’s questionable positioning.
But the Frenchman twice fired over from close range before unmarked strike partner Kevin Gameiro missed with a header.
The Andalusian hosts added to Escudero's early strike after the break to regain the lead when Banega converted his spot kick after Saul Niguez was adjudged to have fouled Joaquin Correa.
Atletico forward Angel Correa then missed a gilt-edged chance to level again as Rico thwarted him in a one-on-one situation and was made to pay when Sarabia rounded off the scoring on the counter-attack 10 minutes from time.
The 2013 King's Cup winners Atletico, who trail Liga leaders Barcelona by 11 points, must now turn their attention to the Europa League where they are in the round of 32 after being knocked out of the Champions League at the first hurdle.
(Editing by Ken Ferris)
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