Diego Simeone's star striker was on target once again, scoring the only goal of the game as the hosts returned to the top of La Liga after two hours back in second place
Winning without playing in top gear is often heralded as a hallmark of a champion, and Diego Simeone's side is well-placed for the title on that basis, with Real Madrid's 2-1 defeat at Sevilla putting the Rojiblancos clear at the top.
Atleti struggled to break down its opponents in a frustrating first half that saw Arda Turan go closest, but top scorer Diego Costa came to the rescue after 63 minutes with his 24th Liga goal of the season.
Real's defeat means Atleti is now a point clear of Barcelona as the advantage in the title race continues to swing between the three teams.
Arda had the hosts' best chances in the opening stages, first prodding wide after David Villa's near-post flick was blocked and then skewing a poor effort off target from 20 yards.
The visitors were quick out of the blocks in the second half, Recio and Jeison Murillo somehow failing to turn Fran Rico's corner home.
But Atleti finally got its act together just after the hour as Costa put his team ahead.
Having seen Roberto keep out a firm header from Gabi's corner just two minutes earlier, Costa met another delivery from the home captain and got his effort beyond the veteran goalkeeper to raise the volume in the Vicente Calderon once again.
Atleti looked to see the game out with a much more disciplined showing after the goal. The players may have been buoyed as a roar went around the ground 75 minutes in as news of Real going behind filtered through the crowd.
Roberto did well to deny Gabi and substitute Diego as Atleti pushed for a second to clinch the result, but the home side was ultimately left to settle for the narrow scoreline.
The hard-fought three points could prove crucial come the season's conclusion for Atleti, as Simeone's side seeks its first league crown since 1996.