The England international marked just his fourth appearance of the season with his first goals since April when on loan at Crystal Palace, and his first in a Blues shirt since April 2016.
Aleksey Rios pulled a goal back for the visitors in the final 10 minutes, but it was job done for Chelsea by that stage as they moved to nine points from nine in Group L thanks to a stellar display from fringe man Loftus-Cheek.
Loftus-Cheek required a little over a minute to get off the mark with his first goal in European competition, guiding the ball past Denis Scherbitski from 12 yards at the end of a Davide Zappacosta cutback.
BATE barely got the ball out of their own half in the early stages and they were two down before mounting their first serious attack, as Loftus-Cheek this time got in front of his marker to turn Willian's corner into the back of the net.
Those two goals, coming from Loftus-Cheek's first on-target shots of the season, ensured that the home side were in complete control right from the off.
Pedro curled a deflected shot agonisingly wide, and Mateo Kovacic - one of three Chelsea players to retain their spot in the side from Saturday's 2-2 draw with Manchester United - prodded wide from closer range as he attempted to join Loftus-Cheek in getting off the mark for the season.
Willian then volleyed over the crossbar with an awkward volley and sent a tame attempt down the middle for Scherbitski to deal with, while Loftus-Cheek glanced wide from a promising position from Zappacosta's latest cutback later in the first half.
The Blues' best opportunity to add to their scoring before half time came via a front-post flick-on, which Andreas Christensen inadvertently stopped on the line.
Loftus-Cheek killed off the tie for good from Chelsea's first opening of the second period, though, by side footing the ball into the bottom corner from just outside the box.
Another of Chelsea's subs in Victor Moses nearly added a fourth, seeing his shot saved down low by Scherbitski, but BATE - 12-in-a-row champions of their domestic league - were unperturbed as Mirko Ivanic tested Kepa Arrizabalaga for the first time with a quarter of the game to play.
Scherbitski was again required to thwart Zappacosta from long range, before pushing aside Olivier Giroud's shot on the spin as the Frenchman's scoreless run continued.
BATE, thumped 6-0 by Arsenal at this same stage last season, pulled one back through Rios's tap-in 10 minutes from the end when a deep delivery was allowed to drop at the back post - the first goal Chelsea have conceded in Europe this term.
Chelsea comfortably saw through the remaining minutes to make it three group-stage wins in a row to begin a European campaign for the first time since 2010, leaving them on the brink of a place in the last 32 as they hold a six-point advantage over the three sides below them at the midway point.
CHELSEA (4-3-3): Kepa; Zappacosta, Cahill, Christensen, Emerson; Fabregas, Kovacic (Kante 77'), Loftus-Cheek; Willian (Moses 57'), Pedro (Hudson-Odoi 60'), Giroud
BATE BORISOV (4-3-3): Scherbitski; Rios, Filipovic, Filipenko, Volodko; Baga (Yablonski 76'), Dragun, Hleb (Ivanic 55'); Skavysh, Signevich (Tuominen 71'), Stasevich