The win on Saturday lifts Atleti to 19 points, the same as league leaders Barcelona, who have a better goal difference. They are also a point better than capital rivals Real Madrid, though both Barca and the Blancos have a game in hand.
The visitors, meanwhile, extended their winless streak to five despite enjoying an edge on possession and making the better start, reports Efe news.
Only a stupendous effort by home goalkeeper Jan Oblak kept Athletic from taking the lead in the second minute on a potent header from Inigo Martinez on Saturday.
The Slovene leaped to nudge the shot just over the cross-bar.
Athletic set the pace, moving the ball with relative ease, but struggled to penetrate the Colchonero defense after that early chance.
A last-second poke by Koke prevented what looked like a sure goal for Athletic's Inaki Williams before Oblak made another fine stop against Raul Garcia.
As the match clock approached the half-hour mark, Saul Niguez put Atleti up 1-0 in the culmination of a give and go with Angel Correa.
Coming against the run of play, the goal lifted Atletico and their supporters, while leaving Athletic at a loss for how to respond.
The Bilbao side maintained their advantage on possession after the re-start, but Oblak was never troubled again and the Colchoneros nailed down all three points with Alvaro Morata goal's in the 64th minute, as Correa picked up his second assist of the night.
Saul nearly added a third goal in stoppage time.
The loss, Athletic's fourth of the season, leaves the Bilbao club in 10th place, with 13 points.
( With inputs from IANS )