Diego Simeone's side, fourth, moved six points clear of their Basque opponents, fifth, with five matches remaining.
After European elimination and then a woeful defeat at Alaves last weekend in the top flight, Atletico got back on track with strikes from Rodrigo De Paul and Angel Correa, as well as an Unai Simon own goal.
Nico Williams had levelled De Paul's opener in the first half for Athletic, minutes after suffering alleged racial abuse as he went to take a corner.
Defeat leaves Copa del Rey winners Athletic unlikely to return to the Champions League for the first time in a decade.
Earlier Girona moved second with a 2-0 win at Las Palmas, putting themselves on the verge of Champions League qualification.
Barcelona, third, host Valencia on Monday while runaway leaders Real Madrid beat Real Sociedad 1-0 on Friday.
Atletico fans greeted visiting Los Leones forward Raul Garcia, retiring at the end of the season, with a tribute. He was part of their squad that won La Liga in 2014.
Inaki Williams hammered an early effort off target for the visitors before Atletico took the lead against the team which has beaten them three times already this season.
A poor clearance fell to the feet of De Paul on the edge of the box and the Argentine fired home with the help of a significant deflection off Ruiz de Galarreta.
Spain international Oihan Sancet fired narrowly off target as Athletic pushed for an equaliser.
The game was paused momentarily after apparent racial abuse was levelled at Athletic winger Nico Williams when he went to take a corner in the 36th minute.
Moments before half-time, he responded with a goal, finishing calmly after Antoine Griezmann gave the ball away to spark an Athletic counter-attack.
Nico Williams celebrated by tapping his arm in celebration, an apparent reference to his skin colour after the abuse.
Atletico pulled back ahead in the second half when Correa controlled Koke's chipped ball over the top well and then stayed composed to beat Simon.
The hosts made the game safe when Samuel Lino hit the post with a low shot and the ball ricocheted in via the back of goalkeeper Simon.
