Ander Herrera hit the net from a free kick with 14 minutes remaining 76 minutes after Mikel San Jose and Oscar de Marcos had struck.
Bilbao are now nine points clear of Europa League finalists Sevilla in the battle for fourth spot in La Liga.
Ernesto Valverde's side have a better goal difference than Sevilla, who have three games left of their campaign.
- Sports & Recreation
- Europa League
- Ander Herrera