The home side started the game well and pushed forward early on, with David Villa coming close with a header on seven minutes.
© Getty Images
Diego Costa made room for a shot three minutes later, but his effort went wide of the post.
Atletico were awarded a penalty on 25 minutes after a foul by David Costas, although Costa's spot kick was saved well by the goalkeeper.
Costa gave the home side the lead on 43 minutes, turning a cross in from close range to make it 1-0.
Villa had a huge chance to double the lead on the hour mark, but he could only put his shot wide of the post.
Two minutes later, Costa did grab a second goal, muscling past two defenders before firing his shot into the back of the net.
Nolito pulled a goal back for the away side on 71 minutes through Nolito, who chipped over the onrushing goalkeeper to make it 2-1.