The visitors took the lead five minutes before half time after alert play from former Newcastle striker Obafemi Martins. The Nigerian pounced on a loose ball before rounding the keeper and sliding it into the open goal.
The hosts were handed a perfect chance to get an equaliser just 10 minutes after the restart when Pedro Lopez was adjudged to have handled inside the box. The referee awarded the penalty and showed Lopez his second yellow card to reduce Levante to 10 men.
Riki stepped up to the spot kick but blasted his effort high over the bar to ensure that the score remained 1-0.
Deportivo's night then went from bad to worse as goalkeeper Daniel Arazubia was given his marching orders following a foul on Martins. The hosts had already made all three subs, so Javi Camunas donned the gloves and went in goal for the remainder.
The winger could not keep Levante out for too long as Barkero fired an effort into the bottom corner with just eight minutes left on the clock to kill the game off.