Levante were trailing from the sixth minute after Aritz Aduriz headed Bilbao in front with his 11th goal of the campaign, but the overlapping Christian Lell blasted an equaliser into the top corner after 26.
The visitors had young defender Aymeric Laporte sent off a minute before the break and Vicente Iborra headed in from close range before the teams went in for halftime.
Nabil El Zhar's low shot from outside the area ended the game as a contest in the 69th.
Bilbao's Spain striker Fernando Llorente, who is negotiating a possible move to Juventus, received a warm reception from Levante fans when he came on as a substitute, but was unable to dispel the doubts surrounding Marcelo Bielsa's stewardship of the club.
Bilbao, last season's Copa del Rey and Europa League finalists, are 13th with 21 points.