Getafe were close to opening the scoring less than five minutes in when Pablo Sarabia rounded a couple of defenders before unleashing a powerful strike from the edge of the box, but Gorka Iraizoz made the save.
Aritz Aduriz had the first sight at goal for Bilbao midway through the first half as he met a cross in the box, but his header failed to trouble the goalkeeper.
Baba Diawara had a chance to get the home side back on level terms early in the second half when he tried to lash the ball in from a high ball in, but Iraizoz was on hand to make the stop.
Chances were at a premium for the remainder of the second half, but the visitors came close to putting the win beyond doubt inside the final 10 minutes when Gomez Perez Ibai tried to fire in from a free kick just outside the box, narrowly missing the post.
Etxebarria appeared to have sealed the points in the final minute of normal time with a powerful free kick which left the goalkeeper rooted to the spot.
Angel Lafita immediately pulled one back down the other end moments later, heading in at the near post, but Emiliano Velazquez was unable to level with the final action of the game, nodding the ball wide.
The result leaves Bilbao ninth in the table, one place above Getafe.