Mikel San Jose’s strike shortly after the restart put Bilbao on course to retain an interest in European competition this season.
And Markel Susaeta made sure of the victory with a late finish after making the most of superb approach work by Borja Viguera.
Both teams went into their final group game with no chance of last-16 qualification, but Bilbao knew that a draw would be enough to ensure they progressed to the Europa League, with the Champions League knockout phase places already filled by FC Porto and Shakhtar Donetsk.
BATE, having collected just three points from five Champions League starts, were given little chance of preventing Bilbao from making progress.
And the home side dominated early on, with Ibai Gomez forcing a good save out of BATE goalkeeper Artem Soroko, before Mikel Rico shot over the bar and Gomez had a header that also failed to find the target.
BATE could make little headway in the game, and their frustration was compounded by Evgeni Yablonski being booked for a bad foul, although Bilbao’s Andoni Iraola also saw yellow for hand ball as the visitors continued to hold out.
But BATE’s resilience could not last, and Bilbao conjured a breakthrough just two minutes after the restart.
And it was San Jose who came up trumps, delivering a fine finish from Susaeta’s corner to put Bilbao firmly on their way to the victory they required to keep alive European competition hopes this season.
BATE now had to throw everything at their opponents, but Bilbao still looked the more dangerous attacking force and Gomez twice forced saves from Soroko before Susaeta made sure of maximum points.