A second-half header from Olivier Giroud - his first goal of the season - proved to be the difference between the sides, although BATE struck the woodwork on three occasions.
Chelsea progress through to the knockout stages, but the Blues still require a point to earn top spot in Group L after Videoton's win against PAOK.
Maurizio Sarri made seven changes to his starting lineup, but the Premier League side started well at the Borisov Arena without being able to create a clear-cut opportunity.
BATE had no such difficulty at the other end and the home side almost went ahead in the 12th minute through Dzmitry Baha, but the midfielder's 25-yard strike hit the post with Kepa Arrizabalaga beaten.
The home side quickly won a corner and the Spaniard had to be alert to keep out Stanislaw Drahun's header, but the two chances resulted in Chelsea becoming more assured on the ball.
However, the Blues were creating very little in the final third, with only a miscued Giroud volley from a floated Ross Barkley pass coming anywhere near to breaking the deadlock.
Giroud also headed marginally wide from a corner shortly before the break, but Sarri cut a frustrated figure as he made his way down the tunnel at half time.
Chelsea went straight onto the front foot after the restart - presumably after some stern words from their head coach - and the visitors found the breakthrough in the 52nd minute as Giroud directed a glancing header inside the near post after meeting Emerson's cross from the left flank.
The Blues were beginning to pose a constant threat, but just before the hour mark Mikalay Signevich almost found an equaliser for BATE with the striker seeing a shot hit the underside of the crossbar after he had got in the way of a scuffed effort from distance.
Alexei Rios was also guilty of squandering a glorious opportunity to get his team back on level terms as the right-back somehow failed to hit the target when being found in space from 12 yards out.
Chelsea were producing one of their least effective performances of the season, but Barkley still came close to netting a second for his side with a 25-yard attempt which was tipped wide by Denis Scherbitsky.
Both sides struggled to create anything of note during the closing stages of the game, although Sarri did hand Callum Hudson-Odoi the chance to gain more experience in the first team with five minutes remaining.
BATE almost snatched a leveller in the third minute of added-on time, but Baha's 20-yard volley struck the post before Chelsea frantically cleared the ball away from danger to see out the remaining seconds for their fourth successive win of the group.
BATE BORISOV (4-3-3): Scherbitski; Rios, Volkov, Filipenko, Filipovic; Baha, Dragun, Hleb (Berezkin 81'); Skavysh (Moukam 76'), Signevich (Tuominen 73'), Stasevich
CHELSEA (4-3-3): Arrizabalaga; Zappacosta, Christensen, Cahill, Emerson; Jorginho, Barkley, Loftus-Cheek (Kovacic 64'); Pedro (Hudson-Odoi 85'), Hazard (Willian 62'), Giroud