Neither team could advance to the last 16 after Wednesday's clash, but the hosts knew a draw would be enough to secure their spot in Europe's second-tier competition while only a win would do for BATE.
Aleksandr Yermakovich's men frustrated Athletic until the 47th minute when Mikel San Jose scored the vital opener from a corner and Markel Susaeta added a second late on.
Susaeta's strike also meant BATE hold the unenviable record of conceding the most goals in a Champions League group stage at 24, the previous mark of 22 having been set by Dinamo Zagreb during the 2011-12 season.
BATE's 2-1 victory against Ernesto Valverde's side in the reverse fixture back in September remained the source of the Belarusian club's only points and goals of the group stage.
The visitors attempted to stifle Athletic from the first whistle at San Mames and succeeded in the first half before San Jose's strike settled the nerves and the Spanish side cruised to victory.
Starting without leading scorer Aritz Aduriz, who was injured in domestic action at the weekend, the home side needed a spark.
Ibai Gomez almost provided it as early as the sixth minute when he unleashed a stinging drive from 20 yards, but Artem Soroko acrobatically turned his effort behind.
A familiar pattern of play was soon established as BATE packed men behind the ball and Athletic probed for an opening with Susaeta a constant threat down the visitors' left.
The winger nearly created the opener in the 18th minute, beating two men before cutting back from the byline. Guillermo Fernandez failed to control and when it fell to Ibai, he snatched at his 15-yard shot and fired over.
Valverde's men appeared to be struggling to find a way through.
Oscar de Marcos did go close on 36 minutes, turning smartly to create space on the left-hand side of the box before getting off a powerful effort, but in truth it was straight at Soroko and the goalkeeper was able to push it away.
The home side's frustration did not extend long into the second half, however.
Fernandez appeared to have wasted a great chance to give his side the lead, taking too long to get off a shot and allowing Nemanja Tubic to slide in and block his effort just a minute after the break.
But from the resulting Susaeta corner, captain San Jose was afforded far too much space inside the box to volley past Soroko from eight yards.
The relief was evident and the hosts immediately began to play with more freedom. Ander Iturraspe's clever throughball with the outside of his foot six minutes later put Fernandez in on goal once more and this time the striker struck the post with a left-footed shot on the turn.
BATE showed slightly more ambition after going behind, but lacked the quality to fashion any real openings.
And Susaeta then capped his performance with the goal it deserved, as he converted substitute Borja Viguera's low cross in the 88th minute.
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