Cordoba's 15th straight game without a win left it eight points from safety before the rest of the teams play this round.
Etxebarria's shot went in off a defender in the 56th, while Cordoba missed a number of opportunities.
Misses by Bebe, Angel Crespo and
Cordoba's one bright spot was goalkeeper Juan Carlos Martin's acrobatic save to push Aritz Aduriz's goal-bound header off his bar in first-half injury time.
"The team went out there trying to win today, and we had a lot of chances to score a goal," Martin said. "But we just weren't able to so and they scored off a bounce.
"The only thing left to do is to try and pick ourselves up and keep fighting while we still are mathematically alive."
Bilbao stayed in eighth place and with hopes of moving up into Europa League positions.
Leader Barcelona visits crosstown rival