The Blues have come under pressure for their recent Premier League form but a hat trick from the returning Tammy Abraham ensured there was no chance of a shock at the Bridge.
Chelsea were quick out of the blocks in this one as Frank Lampard’s looked to dodge a banana skin as Abraham fired home from Timo Werner’s blocked shot.
And the returning England star quickly made it 2-0 just after as he powered home Reece James’ cross.
But Luton were in no mood to just fade away before the break as Jordan Clark’s drive was fumbled into the net by Kepa.
However, Chelsea were determined not to let this slip away in the second half as they laid siege to the Luton goal.
The outstanding Abraham finally wrapped it up for Lampard with 15 to go, as he tapped home Callum Hudson-Odoi’s cross, before the luckless Werner was denied from the spot late on.
Full Time from Stamford Bridge it’s Chelsea 3 Luton Town 1