The setback for Hartlepool came just three days after losing at home to Brentford in an FA Cup replay.
Luton soaked up early home pressure without even conceding a chance, and took the lead with the game's first real chance on 20 minutes.
Defender Chris Coyne won possession just inside the home half, and was given the space to run to the edge of the area before placing a perfect low shot home.
Coyne's opposite number in the home defence, Micky Nelson, headed inches over the Luton bar from the restart, but the leaders quickly hit back and Enoch Showunmi lashed a long-range shot just as close to the target.
But the big striker came back for more, and 12 minutes into the second half he began a six-minute spell in which three goals were scored.
He doubled Luton's lead with a good finish from the left of the area after a long free-kick, and Pool assistant manager Martin Scott was sent to the stand by the referee.
But on 61 minutes Adam Boyd's header was cleared off the Luton line, and seconds later the home side narrowed the gap with an own goal off the head of Sol Davis.
But Luton had a quick answer of their own, and on 63 minutes full-back Kevin Foley got away from the defence to score with a low shot from the left of the area.
Home sub Matty Robson raced clear to narrow the gap again as injury time began, but it was too little and too late to save the home team.