Buoyed by their first away win in four months at Hillsborough on Tuesday, Town started well and threatened within 35 seconds when Carlos Edwards volleyed Kevin Nicholls' quickly taken free-kick at Bo Myhill from 14 yards.
The visitors were given a chance to register their first attempt on goal in the sixth minute when Chris Coyne was harshly adjudged to have fouled Jon Parkin on the edge of the area, but Keith Andrews wastefully ballooned the ball over from 20 yards.
Keith Keane gave Town the lead in the ninth minute. The 19-year-old started the move by winning the ball ahead of Kevin Ellison and feeding Ahmet Brkovic, who in turn found Rowan Vine running down the left flank. Keane continued his run into the penalty area and after eventually being found by Vine, swivelled to send a diving header accurately into the far corner from 12 yards.
Hull responded with a Leon Cort header nodded off the line by Kevin Foley after Ellison's deep corner two minutes later, before they levelled matters with a well-worked free-kick routine in the 14th minute. After Coyne had again been pulled up for fouling Parkin, Andrews took the kick, but this time touched in the onrushing Elliott with a reverse pass and the Tigers' Northern Ireland international drilled the ball low into Marlon Beresford's bottom left-hand corner.
The high-tempo start continued as Vine was denied by Cort's well-timed challenge on the edge of the six-yard box in the 15th minute after Foley had knocked back Nicholls' chipped pass and seconds later Town were denied a penalty when Brkovic's left-wing cross appeared to strike the arm of John Welsh.
The visitors gradually began to settle though and ten minutes before the break they were ahead after some slack Hatters defending. Foley first gave the ball away and then found himself the wrong side of Elliott after Parkin had beaten Coyne to the ball, allowing the Hull winger to send in a fierce cross-shot that was gleefully dispatched by Darryl Duffy from a yard out.
There was worse to come for Town three minutes later as Ellison completely outstripped Keane down the Hull right and reached the by-line before pulling back for Parkin to all too easily convert at the near post and leave Hatters shell-shocked at the break.
Steve Howard had started the game hoping for his 100th Luton career goal and it almost came in the 53rd minute when Coyne headed Nicholls' deep free-kick back across goal and Howard sent a left-footed effort over the bar from six yards.
Eleven minutes into the second period boss Mike Newell made a bold move as he carried out a triple substitution, bringing on Dean Morgan for Brkovic, Warren Feeney for Vine and handing David Bell his Town debut in place of Enoch Showunmi.
The changes almost had an immediate effect as Coyne saw his header from Nicholls 59th minute corner nodded off the line before Nicholls then saw a 15-yard drive deflect away off the prone Sam Collins after Howard had nodded down an Edwards cross.
With Hull sitting back, Bell hit a 62nd minute shot that deflected wide off Howard before Howard himself tested Myhill with a 15-yard angled effort.
Luton ploughed on, but their day was just about summed up in the 79th minute when Morgan left substitute Scott Wiseman for dead with a mesmerizing run and then saw his cross-shot spilled into the path of Feeney, only for the Irishman to poke the ball wide from six yards with the goal at his mercy.
The Hatters were given a glimmer of hope, however, four minutes from time when Coyne dived to head home Edwards' cross at the far post for his second of the season, but Hull hung on.