David Hopkin’s rock-bottom side were second best almost throughout the contest as the Hatters roared to a sixth win in seven matches.
It was the in-form Hatters who created the first opportunity when Elliot Lee crashed in a shot which just cleared the crossbar.
Paul Caddis carved out the Bantams’ first chance when he turned neatly before seeing a goal-bound strike blocked.
The hosts struck the opener just before the half-hour mark when Harry Cornick’s initial shot was parried by Richard O’Donnell, only for James Justin to lash in the rebound.
Then, two goals from Lee in five minutes put the game out of reach for the visitors. His first – in the 34th minute – came after Luton made the most of a quick counter-attack before he doubled his tally with a sweet strike into the bottom corner.
David Ball thought he’d grabbed a goal back for Bradford shortly after the restart, but he was thwarted by an offside flag.
The Bantams then threatened when Kelvin Mellor forced James Shea into a brilliant diving save.
Eoin Doyle saw a header saved by Shea, but the Hatters made it four when Cornick raced clear before clipping past O’Donnell.
Luton Town: Shea, Stacey, Justin, Bradley, Pearson, Cornick, Rea, Shinnie, Mpanzu, Collins, Lee. Unused substitutes: Stech, Jones, Potts, Grant, Sheehan, Hylton, Jarvis.
Bradford City: O’Donnell, Ball, McGowan, Wood (Payne, 53), Chicksen, Henry, Mellor, L O’Brien, Caddis, Doyle (Miller, 75), Bruenker (J O’Brien, 46). Unused substitutes: Wilson, Isherwood, Devine, Colville.
Referee: Antony Coggins