Olivier Giroud scored his first goal for Chelsea in the 2018/2019 to Chelsea progress to the Europa League round of 32 with two games to spare.
It was not an easy encounter for Chelsea in Belarus with Giroud's first goal since May in the 52nd minute the only goal of the game.
The hosts hit the woodwork in both halves and defended stubbornly, which proved problematic for a sluggish Chelsea who failed to register a shot on target in the first half.
After the restart Chelsea opened the scoring through Giroud's header from an Emerson cross in the 52nd Minute.
Jorginho's first-time pass was fizzed in from wide towards Giroud by Emerson, and the France striker's near-post header went underneath Denis Scherbitski's despairing dive for the opener.
The Belarusian side, who had never beaten an English team on home soil, went in immediate search of an equaliser and nearly found it six minutes after falling behind, when Nilokai Signevich struck the bar after turning Dagun's long-range shot into one of his own.
For BATE, it was a strong performance against the only unbeaten side left in Europe, but Chelsea now need only a point from their two remaining games to win Group L.
Chelsea have won four consecutive games in European competition for the first time since April 2012, when they went on to win the Champions League.
Maurizio Sarri has won all 10 of his Europa League group stage games as a manager, with his sides scoring 28 goals while conceding just four in return.