Chelsea wasted no time in taking the action to the half of Luton with Malo Gusto making crucial incursions down the right side of attack.
England international, Rahim Sterling slalomed past Luton defenders from the left side to slot home the opener with his left foot on the 17th minute.
Sterling increased the tally for the Blues on the 68th minute after tapping in a low cross from winger, Malo Gusto on the right side of attack.
Senegal striker, Nicolas Jackson finally ended his goal drought in tow game – latching onto a low right cross to prod the ball behind Thomas Kaminski in post for Luton.
The Gambian born, 22, has found the net once in three games with no assist yet on cards.