Atletico Madrid continues winning ways
Adrian Lopez had spurned the best chance of a largely uneventful first half but the holders went in front just two minutes after the restart when Costa hooked in Tiago's flick-on from Gabi's corner.
The goal brought the Portuguese side out of their shell a little but any hope they had of heading back across the Iberian border with a point were extinguished 23 minutes from time when Emre curled a sumptuous free-kick into the top corner and, despite a late consolation goal from Salim Cisse, Atleti saw out the final few minutes with relative ease.
Diego Simeone's men have now also recorded 11 consecutive victories in all competitions stretching back to the opening day of the season and they almost certainly ensured their place in Europe after Christmas with a competent display despite resting six first-team regulars.
The most notable absentee was Radamel Falcao and had the Colombian been on the field Atleti would surely have been ahead inside two minutes. Koke retrieved a ball wide on the right and after his driven cross was missed on the stretch by Costa, Adrian Lopez could not turn the ball home at the back post.
Sergio Asenjo was then forced into a routine save to deny Edinho on a rare dangerous counter-attack by the visitors and Atleti were restricted to efforts from range for the remainder of the half.
Koke tested Ricardo from fully 30 yards with a shot that the keeper parried away to safety before Emre went even closer with a bending effort that whistled just past the post.
However, for all their good work in the first half, Academica were quickly undone in the second by some shocking marking as Costa was left in acres of space from a corner on the right to volley home his third goal of the season.
The Brazilian was denied a second five minutes later as Ricardo produced a fine double save to beat away his fierce effort and get back on his feet to smother Adrian's header from the rebound.
Yet the game seemed safe for the Spaniards when Emre curled the most beautifully precise free-kick into the top corner midway through the half.
However, back came Academica in the final quarter and after Asenjo had made a smart save to turn away Cleyton's free-kick, they did get a goal back from another set-piece as Cisse headed home unmarked inside the area.
Costa should have sealed the points when he headed wide from six yards moments later but it mattered little as despite a late aerial bombardment, Atleti held on to retain their three-point advantage over Viktoria Plzen at the top of Group B.
Academica remain rooted to the bottom of the group alongside Hapoel Tel-Aviv with just a solitary point to their name so far.