The Blues dominated possession in the first half but struggled to create chances against a well-organised home side.
The hosts came the closest to opening the scoring in the first 45 minutes when Dmitri Baga's shot beat goalkeeper Kepa Arrizabalaga but crashed against the post.
Chelsea broke the deadlock six minutes into the second half. Emerson Palmieri sent in a cross from the left, and Olivier Giroud headed home his first goal under Maurizio Sarri.
BATE did have chances to equalise—Nikolai Signevich hit the woodwork, while Alexei Rios blazed a fine chance over with the goal gaping.
The result means Chelsea top Group G with 12 points, while a third defeat sees BATE Borisov stay bottom on three points.
Giroud Doesn't Deserve to Pass Morata in Chelsea Pecking Order
Giroud finally ended his long scoring drought against BATE, notching his first goal since May. Opta noted exactly how long he'd gone without finding the back of the net:
It was the breakthrough Chelsea needed. The Blues had dominated possession in Belarus but had found it tough going breaking down the hosts:
Nizaar Kinsella @NizaarKinsella
Chelsea had 78.4% possession in that half. 6 shots but not hit the target yet, unlike BATE. Hazard has not had a shot but has had some good dribbles and passes. Emerson probably the best player in that half but perhaps complacency is leading to sloppy play at both ends. #CFC
The goal will no doubt bring relief and help restore Giroud's confidence in front of goal. The Frenchman has made 12 appearances this season, contributing four assists.
His lack of goals has seen him slip behind Alvaro Morata in the pecking order. The Spaniard was left out of the trip to BATE because Sarri "thought it better to rest at Cobham and have good training," per Tom Olver at Metro.
Morata should return to the starting XI for Sunday's visit from Everton. The striker is on a good run of form and has five goals in his last six appearances for the Blues.
The 26-year-old has failed to fully live up to expectations since arriving at Chelsea from Real Madrid in 2017. His goals dried up and he fell out of favour under previous manager Antonio Conte at the end of his first season.
Morata has opened up on his difficulties at the club:
He also struggled for goals at the start of this season, scoring just once in his first nine outings for the Blues.
Goal's Nizaar Kinsella showed how he's been forced to adapt his game at Stamford Bridge:
Doubts still remain over whether Morata is a title-winning striker, but he has rediscovered his goalscoring touch in recent weeks and deserves to continue as first choice over Giroud.
BATE face Gorodeya in the Belarusian Cup on Saturday. Chelsea are back in action on Sunday when they host Everton at Stamford Bridge in the Premier League.