Drew Talbot's second-half goal wasn't enough as earlier strikes from David Livermore and Michael Turner gave City the win and left the Hatters in the drop zone.
After Saturday's depressing defeat to Leeds, Town boss Mike Newell gambled by moving centre-half Leon Barnett up front and dropping skipper Steve Robinson and strikers Bjorn Runstrom and Warren Feeney.
In came Kevin Foley, Richard Langley and Talbot, while Markus Heikkinen took the captain's armband.
Barnett's presence in the final third prompted Town to start in direct fashion, but when they did get the ball down they created an opening as Keith Keane played a one-two with Foley before hitting a 20-yard volley at Boaz Myhill in the 12th minute.
The game meandered on in scrappy fashion until a rare moment of quality produced the opening goal as right-back Sam Ricketts teased his way to the byline in the 22nd minute and produced the perfect cross for Livermore to nod home from eight yards.
The Hatters seemed unable to mount any response and instead Hull came forward with Bolton loanee Ricardo Vaz Te lashing over from 25 yards after a 26th minute Dean Windass knock down, before Turner headed Livermore's corner just wide four minutes later.
Things got even worse for Luton in the 34th minute as goalkeeper Marlon Beresford came off worse after a goalmouth scramble and had to be stretchered from the field with a head injury.
After being jeered off at half-time, Town reshuffled for the second period by bringing on Feeney for Richard Langley and moving Barnett into midfield.
It sparked a brief rally as Carlisle and Heikkinen both just failed to convert a 49th minute Lewis Emanuel free-kick from the right.
But the Hatters were stunned just after the hour mark when Turner produced a finish unexpected for a centre-half by volleying Livermore's free-kick into the corner from the edge of the area to make it 2-0.
With Luton reeling, City came again as firstly Windass and then Vaz Te both fired wide from 20-yards.
As the game appeared to be slipping away, Luton were thrown a lifeline in the 70th minute when Carlisle was clattered on the edge of the box and substitute Dean Morgan stepped up to whip in a curling free-kick that was nodded home by Talbot for his third Luton goal.
Gaps developed as Town desperately pushed on for an equaliser and Vaz Te should have wrapped things up for Hull in the 76th minute when he ran clear on to Livermore's pass only to fire past the post with just Dean Brill to beat.
Vaz Te was denied by Brill before Feeney forced Myhill into a fingertip save in the 82nd minute.