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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.