The Blues, inspired by their England midfielder, were far too strong for their opponents, stretching their lead at the top of Group L to six points with three games to play.
Loftus-Cheek swept Maurizio Sarri’s side ahead with just one minute and 42 seconds on the clock after being picked out by Davide Zappacosta’s low cross.
The 22-year-old doubled the lead with a side-foot volley from Willian’s corner and sealed his first competitive hat-trick with a sumptuous 20-yard finish before Aleksei Rios scored a consolation.
Bate goalkeeper Denis Scherbitski produced sublime saves to keep out Zappacosta and Olivier Giroud as Chelsea dominated from start to finish.
Can Loftus-Cheek force his way into the side?
He grasped the opportunity with both hands after Sarri made eight changes to the side that started the 2-2 draw with Manchester United last Saturday.
He has been limited to just 33 minutes of top-flight action since the Italian took charge in the summer.
In contrast, N’Golo Kante and Jorginho have played every minute of every league game, while Mateo Kovacic has managed 476 minutes.
Meanwhile, Ross Barkley has clocked up more than 300 minutes in the engine room this season, earning himself an England recall.
With Chelsea making an unbeaten start under Sarri, Loftus-Cheek could well have to remain patient or consider another loan move in the January transfer window after impressing at Crystal Palace last season.
There certainly won’t be a lack of interest should the Blues’ boss sanction a temporary switch – especially after this highly impressive performance.
Thirteen unbeaten under Sarri
Bate Borisov looked on a hiding to nothing after falling 2-0 down inside eight minutes.
Chelsea should have won by more but after cruising into a 3-0 lead before the hour mark, they eased off and the visitors were able to score when slack marking let in Rios after a corner.
Sarri was angry his side allowed Borisov to score – a sign of the high standards the former Napoli boss expects at Stamford Bridge.
Much tougher tests lie in wait – Tottenham at Wembley on 24 November and Manchester City at Stamford Bridge on 8 December – yet Chelsea continue to thrive under Sarri.
They are now unbeaten in 13 games this season, third in the Premier League table, in the last 16 of the Carabao Cup – after negotiating a tricky tie at Liverpool – and could book their place in the last 32 of the Europa League with two group games to spare.
Chelsea face two Premier League games – away to Burnley and home to Crystal Palace – and a Carabao Cup tie against Frank Lampard’s Derby County before travelling to Belarus for the return match against Bate Borisov on 8 November (17:55 GMT).