Unai Emery's men were miserable in the away leg last week as they were beaten 1-0, but an aggregate 3-1 triumph was secured with a minimum of fuss after cancelling out the deficit early.
Zakhar Volkov's own goal was followed by a second from Shkodran Mustafi before the interval, with Sokratis Papastathopoulos then making sure on the hour.
Visitors BATE offered little in response and Emery was able to breathe easily as his side chased further goals in a competition that may yet define his first season in London.
BATE had already survived a couple of early scares when, with four minutes on the clock, Pierre-Emerick Aubameyang tore down the right and centred, seeing Volkov stab awkwardly into his own net after Egor Filipenko failed to clear at the near post.
Apparently unable to shut up shop, the visitors then went on the offensive and Stephan Lichtsteiner was required to scramble clear from the Arsenal goal line as Stanislav Dragun found himself unmarked.
That opportunity only briefly disrupted Arsenal's dominance, though, and they edged in front in the tie for the first time before the break, with Mustafi powering home a header from Granit Xhaka's corner.
The Gunners' momentum slowed following the restart, but another Xhaka corner led to the nerve-settling third as Denis Scherbitski charged out and was beaten in the air by towering fit-again substitute Sokratis.
Aubameyang was among those to pass up further opportunities to bolster the scoreline, yet Arsenal's advantage was never in trouble.
What does it mean? Arsenal still alive
While Arsenal are still in the hunt for the top four in the Premier League, Manchester United's upturn in form could see the Gunners on the outside looking in once more. As was the case last season under Arsene Wenger, Emery's side might end up targeting Europa League glory as the most likely route back to the Champions League. Defeat to BATE would have had the head coach facing some very awkward questions, but they battle on.
Iwobi the spark for Gunners
Emery told Mesut Ozil ahead of this match that it was up to him to prove his worth after time out of the starting XI. But Alex Iwobi was Arsenal's creative force during the early stages as they sought a swift breakthrough. He quickly forced a save from Scherbitski and almost curled in a gorgeous second after the own goal, with his movement causing BATE persistent problems.
Another Koscielny blow
Laurent Koscielny has suffered with injury after injury over recent seasons and he provided further concern early in the second half as he bowed out for Sokratis, seemingly suffering with another ailment. The Gunners captain had scarcely been tested, but this went down as another difficult night.
Arsenal are in action at the same time as United on Sunday, hoping for Liverpool to do them a favour at Old Trafford as Emery's side host Southampton. The Gunners will breach the top four if they better United's result. BATE contest the Belarusian Super Cup against Dinamo Brest a week on Saturday.