BATE pulled off a stunning win over the Spanish club.
The Belarusian champion marked the Borisov Arena's maiden Champions league tie with a stirring performance that went some way to putting right the 6-0 defeat at Porto in Group H.
BATE controlled the first half and roused the passionate home crowd after 19 minutes through Denis Polyakov's close-range strike.
The lively Nikolay Signevich's wonderful volley then hit the post but Aleksandr Karnitski's deflected effort doubled the home side's advantage.
Aritz Aduriz pulled one back just before halftime but BATE looked the more likely to score next, with Signevich going close.
The club maintained its advantage to record a first win in the competition since Oct. 2012, with Bilbao's miserable start to the season continuing.
After a tight opening to the game, the BATE fans were sent into raptures with 19 minutes gone as Maksim Volodko's near-post corner was flicked into the path of the unmarked Polyakov and he volleyed home from close range.
Bilbao has only scored once in its five previous matches and struggled to make inroads in the first half. Even when Benat was allowed to chest the ball down under no pressure, he could only fire wide.
But the home side was inches away from doubling the advantage as Karnitski's cross was met by a sumptuous Signevich volley on the right that cannoned back off the post with Gorka Iraizoz well beaten.
The club got a well-deserved second after 41 minutes as Signevich fed Karnitski, who created space with a neat flick 15 yards out and, though his shot was weak, a wicked deflection off Andoni Iraola wrong-footed Iraizoz as the ball spun in at the near post.
The home team was all over Bilbao but the Liga side got back in it a minute before halftime as Iker Muniain's wonderful control allowed him to feed Aduriz, and he fired past Sergey Chernik from 12 yards for his fifth goal of the season.
Signevich proved a real handful and could have added to the lead soon after half-time but his precise effort was weak and Iraizoz made the save.
The host almost caught Bilbao sleeping again after 56 minutes when a quick throw-in found Maksim Volodko in the area but he could not hit the target.
Signevich could have wrapped it up 20 minutes from time as Ander Iturraspe was dispossessed but he got the ball stuck under his feet and saw his shot diverted over, with BATE seeing the game out to record a memorable triumph.