Goal sensation Adrian Forbes ruined his chances of a second FA Cup hat-trick with an injury-time penalty miss but his double condemned Bradford to another miserable exit.
Luton's winger turned striker, who bagged three against Thurrock in the first round, wrecked Bryan Robson's hopes of more cup glory and the ex-Manchester United skipper now faces a grim battle to avoid relegation from the first division.
Robson, who lifted the cup three times with the Reds Devils, had hoped that some of his good luck would rub off on City but they rarely looked like ending a run of three successive third round exits.
In fact the home side failed to muster a shot on target in the first 45 minutes and it was no surprise when their second division rivals snatched a deserved opener after 19 minutes.
Luton's teenage full-back Kevin Foley snuffed out a City attack on the edge of his own box and when his clearance fell to striker Steven Howard, he easily shrugged off his marker.
The hard-running frontman picked out Forbes with a precise pass and he rounded the keeper before firing home into an empty net.
With skipper Chris Coyne in commanding from at the back Luton were hardly stretched although they had one narrow escape when an offside flag halted City striker Alun Armstrong as he sprinted clear.
Luton midfielders Steve Robinson and Matthew Spring both tested Alan Combe with long-range efforts and it took an excellent save by the City keeper to push a Robinson free-kick on to the bar.
Within three minutes of the break Forbes had struck again as Bradford failed to deal with a Robinson free-kick and he pounced to rifle the loose ball home from inside the six-yard box.
Bradford striker Dean Windass rattled the visitors bar with a header and Luton midfielder Ahmet Brkovic cleared a Mark Bower effort off the line before Bradford finally got a break with seven minutes to go.
Luton full back Sol Davis was adjudged to have tugged Windass as he darted into the box and Andy Gray gave City hope with a coolly taken right-footed penalty.
Forbes could still have had the last word after Jason Gavin tripped Howard in the dying minutes but his weak spot kick was smothered by Combe.