Man-of-the-match Leon Barnett's first senior goal for the Hatters gave the hosts the perfect start in the eighth minute and World Cup star Carlos Edwards secured the points 11 minutes from time.
A lively encounter also saw Town hit the post while the Foxes twice rattled the woodwork.
In traditional season-opening sunshine, the Hatters began at their usual breakneck pace and should have opened the scoring in the fourth minute.
Lewis Emanuel almost made it a debut to remember when he robbed visiting full-back Richard Stearman and raced into the penalty area only to pull his left-foot shot onto the outside of the post.
Leicester went close two minutes later when Patrick McCarthy crashed a ten-yard near post header against the top of the crossbar from Gareth Williams' corner.
But it was Luton who opened the scoring in the seventh minute as, after Warren Feeney's hard work down the left had earned a corner, Emanuel centred for Barnett to powerfully head home, unmarked 15 yards out.
The end-to-end action continued as Marlon Beresford denied the Foxes an equaliser with a breathtaking save from Williams' 22-yard free-kick.
Robinson was harshly pulled up for a foul on Alan Maybury to create the opportunity, which saw Williams' curling effort pushed on to the bar by Beresford before the goalkeeper saved the follow up from Matt Fryatt.
The second-half action was interrupted by a flurry of bookings before Town came close to doubling their advantage just before the hour-mark.
Vine's mazy run looked to have come to nothing when he mis-hit his shot on the edge of the area, but the ball fell into the path of Feeney who saw his close-range effort well blocked by Henderson.
New signing Boyd entered the fray for Vine in the 62nd minute and went close three minutes later when he headed Feeney's flick on just wide from a deep free-kick.
Leicester were reduced to long-range efforts although they almost profited when substitute Elvis Hammond robbed Sol Davis and saw his shot deflected wide in the 71st minute.
But it was Luton who got their second in the 79th minute when Feeney ran at the retreating defence and the ball bobbled to Edwards, who cut inside the onrushing McCarthy before toe-poking past Henderson from seven yards.