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 Fede Cartabia in the second half earned them jeers from the stands as Cordoba remained with just one home victory this season.
Bilbao stayed in eighth place and with hopes of moving up into Europa League positions.
Leader Barcelona visits crosstown rival Espanyol on Saturday aiming to protect its two-point lead over Real Madrid, which visits Celta Vigo on Sunday.