Carlos Edwards finished from a tight angle to put Luton ahead in the 12th minute but Hayden Foxe's header ensured honours were even at half-time.
Two goals in three minutes - a chested effort from Rowan Vine and a David Bell strike - put the home side in control.
A Markus Heikkinen header made it 4-1 and Edwards turned in Vine's deflected cross to complete Leeds' misery.
Luton boss Mike Newell:
"I imagine it will have been a long time since Luton beat a club like Leeds 5-1.
"We started quite well and, although they came back into the match towards the end of the first half, we felt that if we could score the second goal, more would follow.
"But we did not expect to get five. Given the way we have been playing at home, and the results Leeds have had, we felt we could beat them."
Luton: Beresford, Heikkinen, Barnett, Foley, Davis, Robinson (O'Leary 81), Morgan (Keane 84), Edwards, Bell, Vine, Feeney (Boyd 82).
Subs Not Used: Brill, Langley.
Goals: Edwards 12, Vine 55, Bell 56, Heikkinen 73, Edwards 90.
Leeds: Sullivan, Kelly, Crainey, Foxe, Butler, Westlake (Lewis 71), Douglas, Derry, Johnson, Cresswell (Moore 72), Blake (Healy 63).
Subs Not Used: Warner, Richardson.
Booked: Westlake, Foxe.
Goals: Foxe 17.
Att: 10,260
Ref: G Hedgley (Bishop's Stortford).