The Hatters beat Huddersfield Town 2-0 on Friday and are now within two points of safety, while QPR lost for a fifth time in six games and are down in 16th.
Luton looked dead and buried after losing 5-0 at home to Reading a little over a week ago, a result that left them bottom of the table and four points adrift of safety.
A 1-1 home draw against Barnsley did little to ease their relegation concerns, but Friday's victory against fellow strugglers Huddersfield has given them plenty of hope.
Helped by teams around them struggling to pick up wins, Town are now potentially just one victory away from climbing out of the bottom three for the first time since before Christmas.
Indeed, given that Wigan Athletic are facing a 12-point deduction for entering administration, finishing in 22nd place - currently occupied by Hull City, one point better off - may be enough for Luton.
Nathan Jones will be targeting all three points on Tuesday evening when a QPR side with no real sense of direction visit Kenilworth Road.
The Rs were six points off the playoffs when the Championship resumed last month, but three points from 18 since the restart leaves them 11 points adrift.
Indeed, the gap on the relegation zone is now only eight points following the 3-0 loss to Sheffield Wednesday on Saturday, so they are now looking over their shoulder.
Only Birmingham City are in worse form than QPR, though they have performed better on their travels than at home of late.
Mark Warburton's men have lost only two of their last six away matches, recording victories away at Preston North End and Middlesbrough in that run.
One more win will make certain of a mid-table finish for QPR, but Warburton now faces a battle getting supporters back on his side following this alarming slump in form.
Warburton described his players as "boyish" in their home loss to Sheffield Wednesday at the weekend. A similar display on Tuesday and QPR really will be in serious trouble.
Luton Town's Championship form: DWDLDW
Queens Park Rangers' Championship form: LLLWLL
Kazenga LuaLua recovered from a knee injury in time to feature from the bench against Huddersfield and is pushing for a recall here.
After picking up such an impressive win in Yorkshire, Jones may well be tempted to go with the same XI for the second match running.
As for QPR, Jordan Hugill has missed the last couple of games with a knock and remains doubtful for this trip to Kenilworth Road.
Warburton went with three at the back against Sheffield Wednesday, meaning that Todd Kane dropped to the bench, but he may revert back to a 4-2-3-1 for this one.
Luton Town possible starting lineup:
Sluga; Bree, Carter-Vickers, Bradley, Potts; Mpanzu; Shinnie, Berry, Lee; Collins, Cornick
Queens Park Rangers possible starting lineup:
Lumley; Kane, Kakay, Barbet, Manning; Cameron, Ball; Oteh, Chair, Eze; Samuel
We say: Luton Town 1-2 Queens Park Rangers
Luton have given themselves a real shot at dodging the drop thanks to their win over Huddersfield. They have failed to win any of their last four home matches, however, while QPR have won two of their last four on their travels, so we are backing the visitors to edge this one.
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