Loftus-Cheek fired the Blues ahead inside two minutes during the meeting with BATE at Stamford Bridge.
Davide Zappacosta cut the ball back from the right and England international Loftus-Cheek emphatically struck a first-time shot into the left corner.
The goal was the 22-year-old’s first for the west London club since he was on target against Aston Villa in April 2016.
And just six minutes later, he doubled the host’s advantage after Willian delivered an outswinging corner from the right and narrowly beat Giroud to the ball to volley home from close range.
Loftus-Cheek capped off his goal rout by completing his hat-trick nine minutes into the second half.
The ball broke to the former Crystal Palace loanee on the edge of the box and his curled effort found the bottom right corner via the fingertips of BATE goalkeeper Denis Scherbitski.
And Loftus-Cheek’s impressive performance has led to fans demanding boss Maurizio Sarri gives him more starting opportunities, beginning with their next Premier League game against Burnley on Sunday.
“If tonight doesn’t show sarri why Loftus-cheek should be starting everyweek what will,” one fan wrote.
Another said: “Damn what a game Loftus-Cheek! Nice strike for the hatty. I think he deserves a start Saturday against Burnley!”
“Surely Ruben Loftus Cheek has to start up front on Sunday. He’s the answer!!!” a third fan commented.
A fourth fan wrote: “Loftus-Cheek better start on Sunday.”