Garcia opened the scoring after just eight minutes when Koke teed up the Spaniard who calmly converted his fourth goal of the campaign.
In-form striker Costa then added the second after 20 minutes when he ran at the heart of the Vienna defence before firing in an effort on the edge of the box.
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Philipp Hosiner nearly pulled one back for the home side when he met a pass with a side-footed effort that hit the woodwork with Thibault Courtois beaten in Atleti's goal.
Following the break Costa added his second of the evening when he Emiliano Insua crossed for the striker to control and finish nine minutes after the restart.