The teams went in level at the interval after an even first period that saw Hayden Foxe, with his first Leeds goal, cancel out Carlos Edwards' opener.
But it was a different story in the second 45 minutes as Town ran riot with further strikes from Rowan Vine, David Bell, Markus Heikkinen and Edwards again.
Luton's Warren Feeney was eager to claim his first league goal since December 2005 and it almost came within 50 seconds of the kick-off after a well-worked Town move.
The Irishman dummied Edwards' throw-in and spun on to Vine's header before smashing an angled 14-yard volley just past the far post.
Feeney then almost got in five minutes later when he charged down Neil Sullivan's clearance from Stephen Crainey's back-pass, but the goalkeeper recovered to claim the ball.
Leeds soaked up Luton's brisk start and created an opening in the eighth minute when Ian Westlake hit a goalbound shot from 12 yards from Adam Johnson's corner, which was hacked away among the mass of bodies in the six-yard area.
Shaun Derry's lofted pass into the area found Robbie Blake in space in the 11th minute, but the former Burnley man could only hit a wild left-footed shot that went out for a throw-in.
Instead it was Luton that went ahead a minute later with some slick play down the right-hand side. Bell found Vine on the touchline, who in turn flicked the ball on for the advancing Edwards.
He seemed to have been stopped by Westlake's tackle, but the ball fell to Vine who instantly slipped in Edwards to round Sullivan and slide home from a tight angle for his fourth of the season.
Leeds could have buckled after the early goal, but they responded positively and drew level in the 17th minute when Johnson, after winning a corner with a burst into the box, crossed for Foxe to head home unchallenged from six yards.
Feeney headed straight at Sullivan two minutes later for Luton after Dean Morgan's teasing run and cross from the left, but as Leeds tightened up, Hatters lost their rhythm.
The next chance didn't come until just before the half-hour mark when Morgan saw his 20-yard drive deflect just wide after Westlake's timely challenge on Edwards in the penalty area.
The second half began at a sedate pace, but soon burst into life when Luton blasted two goals in the space of three minutes.
Feeney was the provider for the first - Luton's second of the day - when he raced on to Kevin Foley's 54th minute pass down the right channel and crossed over Sullivan for Vine to bundle home off his chest from two yards out for his ninth of the season.
Then, moments later, Town raced clear down the right again when Edwards ran on to Feeney's clever pass, beat Paul Butler and squared for Vine to scuff a shot into the path of Bell, who made no mistake from four yards for his second goal in successive home games.
Leeds almost cut the deficit immediately when Butler's header from Johnson's corner was nodded off the line by Sol Davis.
Then, just before the hour, Richard Creswell thought he'd scored after another Johnson corner had only been half-cleared by Luton, but the striker's header hit Foley on the line and Marlon Beresford was able to smother.
As Leeds' efforts faded away, Luton grabbed a fourth when Heikkinen headed home Steve Robinson's deep 73rd minute cross from the right from ten yards.
Edwards got his second of the day to wrap matters up in stoppage time as he touched home Vine's cross from the left.
Another boost for the Hatters was the attendance - a first 10,260 sell-out of the season.