The 23-year-old striker scored either side of an Alvaro Dominguez header to secure a comfortable win and ease the pressure on the club's under-fire boss.
Adrian and Alvaro Dominguez fired Los Rojiblancos into a two-goal lead inside 30 minutes before the young striker added a third with quarter of an hour left on the clock.
Helder Postiga managed to bring the score back to 3-1, but Gregorio Manzano's side held on for a victory which moves it up to ninth in the table while easing the pressure building on the coach.
The home side started proceedings in a confident manner which belied its current poor run of form, with Brazilian Diego pulling the strings in midfield.
After 19 minutes in which Atletico controlled possession without looking particularly threatening, Adrian settled his side's nerves when he opened the scoring with a fantastic header.
Turkish wideman Arda Turan was the architect, drifting in off the right wing before clipping a sumptuous ball towards the penalty spot, where the Atletico No. 7 was perfectly placed to leap and guide a header beyond Roberto in the Zaragoza goal.
Atletico continued to force the issue, and scored the second its play deserved on the half hour. Diego won a free kick on the edge of the box, which Gabi took, floating the set piece towards Diego Godin at the far post. The Uruguayan then forced the ball back across the face of goal, presenting Alvaro Dominguez with the simple task of nodding into an empty net.
Zaragoza, on the other hand, was struggling to offer any sort of attacking threat. This forced isolated frontman, Postiga, to take it upon himself to drag his side back into things.
The Portuguese attempted an ambitious chip from 25 yards which sailed over the bar, before firing off an impressive snapshot which forced a fine reflex save by Thibaut Courtois. However, that was as good as it got for the visitors.
The team was, however, more of an attacking force in the early stages of the second period, and Luis Garcia sent a near-post header wide before flashing a free kick inches over the crossbar in the 53rd minute.
But it failed to sustain the early pressure, and the hosts eventually re-established their dominance in the final 20 minutes, adding their third and final goal in the 74th minute when Filipe Luis drove to the byline and cut back for Adrian to force home a third despite Roberto's best efforts to keep it out.
Postiga pulled one back in the 79th minute when he headed home a Luis Garcia corner, but the goal proved little more than a late consolation as the home side held out for an important victory.
Atletico returns to action on Thursday when it hosts Italians Udinese in the Europa League. Zaragoza, on the other hand, must wait a full week before welcoming Sporting Gijon to La Romareda in its next La Liga fixture.