Richard Cresswell's goal and a late penalty save by Casper Ankergren secured a crucial three points for Leeds in their battle to beat the drop and dragged Luton closer to the Coca-Cola Championship's relegation trapdoor.
Cresswell followed up his goal against Sheffield Wednesday last week with a superbly taken strike six minutes into the second half.
Jamal Johnson played the ball to Cresswell who held up play with his back to goal inside the area on the left-hand side.
It looked like Cresswell would play a neat one-two with Johnson but instead the big striker turned his marker and fired a low left-footed shot across Marlon Beresford and into the bottom corner.
It was just rewards for Leeds after a dominant first-half showing but it looked like Luton would stage an unlikely smash-and-grab raid in the 86th-minute when substitute Drew Talbot was tripped inside the box.
However, Dean Morgan put his spot-kick down the centre of the goal and Ankergren saved it with his trailing leg as he dived to his right. Leeds had the best of the opening 45 minutes but were unable to break down a stubborn Luton rearguard.
Captain Jonathan Douglas came closest to scoring midway through the half when he headed a corner against the Hatters' crossbar and then repeated the trick from the rebound. Cresswell blazed the next rebound into the stand.
Leeds hit the frame of the goal again at the end of the half when Robbie Blake's 25-yard free-kick crashed down off the underside of the crossbar.
On-loan Charlton defender Radostin Kishishev was employed in the centre of the park by Leeds manager Dennis Wise and the Bulgarian displayed his Premiership quality in driving the hosts forward.
It was he who provided the first effort on goal after four minutes with a raking 30-yard drive that narrowly cleared the crossbar.
Soon after Kishishev saw a goalbound right-footed volley headed away from inside the six-yard box by Luton captain Steve Robinson.
Leeds continued to look the livelier side and Johnson was unlucky to see his lob drift past a post after winning the race with Beresford to a long clearance in the 11th-minute.
Sebastien Carole then made Beresford smother a low shot at his near post.
Loan signing Lubomir Michalik made his Leeds debut following his arrival from Bolton. He replaced Rui Marques in the heart of defence.
Wise made four other changes with Ankergren and forward duo Blake and Carole earning recalls while striker Johnson made his first start since his loan switch from Wolves.
Luton manager Mike Newell handed a full debut to loan signing Clarke Carlisle against his former club as he made three changes.
Elsewhere in defence Sol Davis replaced Kevin Foley while Drew Talbot made way for Warren Feeney up front.
Leeds continued to threaten immediately after the break and a swift counter-attack almost resulted in Blake heading home at the far post but the cross was too high.
Cresswell finally made their dominance count with his third goal of the season and his second in as many matches and only a fine block with his feet by Beresford prevented Johnson from doubling Leeds' advantage soon after.
Luton made a double substitution midway through the second half as Feeney and Runstrom made way for Morgan and Talbot but it was Leeds who continued to look most likely to score the next goal.
Michalik's header through a crowded six-yard box sailed agonisingly wide and Blake had a 12-yard shot charged down.
Morgan's missed penalty saw Leeds avenge their 5-1 drubbing at the hands of the Hatters in the reverse fixture at Kenilworth Road back in October.
Teams
Leeds Ankergren, Richardson, Heath, Michalik, Lewis,Carole (Armando Sa 88), Douglas, Kishishev, Blake (Moore 90),Johnson (Healy 85), Cresswell.
Subs Not Used: Stack, Kandol.
Booked: Johnson, Douglas, Michalik.
Goals: Cresswell 50.
Luton Beresford, Keane, Carlisle, Heikkinen, Davis, Bell,Barnett, Robinson, Emanuel, Feeney (Morgan 69),Runstrom (Talbot 69).
Subs Not Used: Brill, Spring, Langley.
Booked: Emanuel, Runstrom.
Att: 27,138
Ref: P Walton (Northamptonshire).