The Premier League side had already guaranteed top spot in Group H, but the Gunners put on a performance in North London with Mathieu Debuchy, Theo Walcott, Jack Wilshere, Olivier Giroud and Mohamed Elneny all getting on the scoresheet.
BATE offered very little, aside from an own goal from Dzyanis Palyakow, and the Belarusian outfit finish bottom of the group.
Arsenal could have taken the lead as early as the third minute when Ainsley Maitland-Niles was teed up inside the penalty area, but the youngster's volley struck the post and went wide.
However, it did not take much longer for Arsenal to move ahead through Debuchy, who drilled a first-time strike into the bottom corner of the net from 18 yards for just his second goal in a Gunners shirt.
BATE were offering nothing at the other end - despite the game being a must-win - and it soon became a case of how many goals could Arsenal manage having previously netting four in the reverse fixture in Belarus.
Just before the break, Wilshere had found himself in more advanced positions and after seeing Scherbitskiy tip a long-range attempt over the bar, the moment came for the midfielder who drilled a 16-yard strike into the far corner of the net for his first Arsenal goal since May 2015.
Both teams began the second half slowly but Arsenal were gifted a fourth thanks to an own goal from Palyakow, who sent the ball into the roof of the net after failing to deal with a cross from Walcott.
Arsenal were soon starting to rack up the chances and Welbeck should have scored a fifth when cutting inside onto his left foot inside the penalty area, but his strike hit Scherbitskiy and rebounded clear.
However, just after the hour, Arsenal extended their advantage when Walcott was fouled inside the penalty area, leaving Giroud with the chance to send the ball into the left corner of Scherbitskiy's net.
To their credit, BATE finally began to offer a response in the final third, but Arsenal scored a sixth in the 74th minute when Elneny curled the ball into the top corner from 14 yards after being set up by Wilshere.
Arsene Wenger took the opportunity to introduce Reiss Nelson, Joe Willock and Eddie Nketiah into the action as Arsenal looked to equal their European scoring record of seven goals, but he watched on as his team struggled to create chances in the final 10 minutes.
BATE came closest during the latter stages, with Mikhail Gordeichuk warming the fingers of David Ospina, but Wenger will be delighted with an emphatic display from his second string ahead of bigger tests in the knockout stages.
ARSENAL (4-3-3): Ospina; Debuchy, Chambers, Holding, Maitland-Niles; Elneny (Willock 77'), Coquelin, Wilshere; Walcott (Nelson 71'), Welbeck (Nketiah 77'), Giroud
BATE BORISOV (4-4-2) Scherbitski; Volodko, Polyakov, Milunovic, Rios; Dragun, Berezkin, Ivanic (Yablonski 76'), Stasevich (Tuominen 69'); Gordeychuk, Rodionov (Signevich 56')