Striker Richard Cresswell had scored a delightful 51st minute goal to keep Leeds' Championship survival hopes flickering.
Lewis Emanuel, Luton's former Bradford City player, had angered Leeds by branding manager Dennis Wise a failure and rating the club's fall from grace worse than Nottingham Forest's.
It added fuel to the fire originally stoked up by Kevin Nicholls' failed bid to quit Leeds and return to Kenilworth Road.
Looking to avenge a 5-1 trouncing at Luton in October, Leeds gave on-loan striker Jemal Johnson his first start and handed a debut to another loanee, Slovak defender Lubo Michalik.
Luton, still without skipper Chris Coyne, struggled to create opportunities for frontmen Warren Feeney and Bjorn Runstrom and the visitors almost fell behind in the sixth minute when they failed to clear Robbie Blake's corner and Radostin Kishishev's goal-bound volley was headed off the line by Sol Davis.
With Leeds enjoying the lion's share of possession, the Hatters had an even bigger let-off on 18 minutes when Michalik and Jonathan Douglas headed against the bar before Matt Heath spooned his 12-yard shot into the crowd.
Matt Heath's glancing header wasn't far wide of the far post, and when Luton keeper Marlon Beresford played Keith Keane into trouble just outside the penalty box, Johnson was booked for colliding with the keeper.
Blake, operating on the Leeds left, was a big danger to Mike Newell's men and, after he was brought down two yards outside the 18-yard box, he saw his free-kick come back off the bar - the third time Leeds had struck the woodwork in a one-sided first half.
The closest Luton came to scoring in the opening 45 minutes was a deflected shot from Emanuel which flew just over the bar and Leeds' intense pressure finally paid off when Cresswell grabbed his second goal in as many games.
Showing excellent close control, Cresswell turned Markus Heikkinen to the left of goal and tucked a low shot wide of Beresford into the bottom right corner.
Leon Barnett should have equalised but miscued with the goal at his mercy and Beresford prevented Leeds increasing their lead with a fine double save from Blake and Cresswell.
Luton must have thought a point was there for the taking when Barnett was brought down by Kishishev inside the box but Morgan's weak shot struck the diving keeper's legs.