Atletico were 2-1 up from the first leg and looked in cruise control as Diego Costa and Radamel Falcao both struck early on.
Jesus Navas pulled one back, and then Ivan Rakitic struck in injury time, but it was too little too late for Sevilla.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.