Diego Simeone made nine changes from the side that lost for the first time this season at Valencia on Saturday and he finally paid for resting his stars in the Europa League as the Portuguese side taught the holders a lesson in taking their chances.
Eduardo pounced on Marinho's excellent ball in to slide past Sergio Asenjo on 28 minutes and the same player sealed the points from the penalty spot 21 minutes from time after Jorge Pulido had brought down Salim Cisse.
Victory keeps Academica's hopes of qualification alive as they move on to four points, whilst Viktoria Plzen and Atletico continue to lead Group B on nine.
Despite making so many changes it was Atleti that had the better of the early stages with Raul Garcia first to threaten but his effort at the end of a flowing move involving Koke and Adrian was bravely deflected over by Joao Real.
The home side then went ahead midway through the half as Silvio was caught sleeping at the back post and Eduardo nipped in front of his man to calmly steer the ball beyond Asenjo.
Atleti started brightly again after the break and Ricardo had to produce a fine save to turn away Koke's effort from the edge of the area before substitute Pedro Martin had appeals from a penalty turned down.
Emre Belozoglu and Garcia saw further efforts fly just off target but the game was settled on 69 minutes when Pulido naively dived in on Cisse inside the area and Eduardo sent Asenjo the wrong way from the resulting spot-kick.