The Hatters continued their 100 per cent start to the season thanks to a long-distance winner from captain Kevin Nicholls.
Luton had suffered a largely frustrating afternoon against a Cherries side that had clearly come for a draw.
But Nicholls gave Town their sixth win on the trot with a curling 25-yard effort nine minutes from time that caught visiting keeper Neil Moss out of position.
It was tough on Moss, who had produced an inspired display to keep the Hatters at bay.
But it was no more than top-of-the-table Town deserved.
Luton began with match-winner-to-be Nicholls testing Moss with a stinging 25-yard drive ten minutes in.
Chris Coyne saw a 33rd minute header palmed on to the bar by Moss after Steve Robinson's corner on the left.
And from another Robinson corner seconds later, Curtis Davies powered a header against the stanchion.
Gareth O'Connor shot narrowly wide for the visitors in the 41st minute before Bournemouth striker Alan Connell placed a header just wide on the stroke of half-time.
Connell threatened again after the interval when he intercepted Marlon Beresford's scuffed goal-kick and raced goalwards, but chipped wastefully over the bar.
Steve Howard saw a 20-yard drive tipped aside by Moss in the 59th minute and two minutes later Rowan Vine ran clean through for Luton, but Moss blocked with his legs.
Vine went close again two minutes later, but just failed to reach Nicholls' cross at the far post.
Bournemouth almost went ahead when Brian Stock's free-kick eluded everyone in the Luton goalmouth, but rolled agonisingly past the post.
Instead it was Nicholls who secured the points for the home side with his moment of magic in the last ten minutes when he collected Steve Robinson's pass, strode forward and found the net from distance.