Raheem Sterling scored two and set up Chelsea's third goal as Luton's Premier League baptism of fire continued with defeat at Stamford Bridge.
The England forward was in inspired form as he set the Blues on their way with a fine solo goal, jinking one way and the other into the box before curling a shot between a gaggle of Luton defenders into the bottom corner.
He swept home a fine first-time finish from Malo Gusto's cross to double Chelsea's lead midway through the second half and then crossed for Nicolas Jackson to poke home his first competitive goal for his new club.
The win was the Blues' first under Mauricio Pochettino, having begun his tenure with a 1-1 draw at home to Liverpool and a shock 3-1 defeat at West Ham last weekend.
Plucky Luton, who lost their first Premier League game 4-1 at Brighton on the opening weekend, had their moments and almost equalised at 1-0 down when Ryan Giles' deflected effort forced a smart reaction save from Robert Sanchez.
But Chelsea were superior throughout and fully deserved their victory - on what was also a winning night for Sporting Life readers who backed Liam Kelly's even-money tip on the Blues to win to nil in his match preview.
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