Markel Susaeta hit the only goal of the game in the 39th minute, and although Athletic were easily the better side, they were unable to extend their lead.
The win sees Ernesto Valverde's men move a step closer to Champions League qualification, while Getafe remain dangerously close to the relegation zone.
With top scorer Aritz Aduriz suspended, it was left to 20-year old striker Guillermo Fernandez to lead the Athletic attack.
The youngster had a lively first half, his header forcing a save from Jordi Codina, and later flashed a shot wide of the far post.
Getafe were second best throughout the game but created a couple of chances.
Angel Lafita rounded Gorka Iraizoz but had too narrow an angle to aim at and could not take advantage. Then Sammir had a go from 20 yards but Iraizoz got down low to make the save.
Athletic took the lead shortly before half-time, Ander Herrera squaring the ball to Susaeta from a free-kick, the forward carefully driving the ball into the top corner.
Herrera could have doubled the lead right before the break, shooting just wide from 40 yards out as Codina scrambled to get back into his goal after failing to clear a through ball to safety.
Fernandez thought he had doubled the lead 10 minutes into the second half when he slid home a low cross by Iker Muniain but he was harshly judged offside.
Getafe were quiet in the second half but still caused Athletic problems, and Iraizoz was forced to tip away a swerving effort from Lafita.
Gaizka Toquero had Athletic's best chance to seal the win, bursting into the box but unable to lift the ball over Codina, and the goalkeeper had to make a late save to deny Oscar de Marcos.