Two goals from Fernando Llorente and one each from Oscar de Marcos and Iker Muniain earned Bilbao a Europa League quarter-final first-leg win at Schalke.
Raul earlier gave Schalke a 2-1 lead with his double, before the Spanish side fought back to earn victory.
Elsewhere, AZ Alkmaar shocked Valencia with a 2-1 victory, while Sporting Lisbon saw off Metalist 2-1.