Steve McNulty's first goal for Luton helped his side defeat lowly Stockport for only their second win in 14 games.
In a first half lacking in quality, Hatters captain McNulty broke the deadlock when he stooped low to head home David Martin's corner.
Simon Ainge came close to doubling the lead when he hit the post with an effort from just outside the area.
But the hosts held on to victory, despite Mark Cullen seeing an effort tipped over the bar for County.
Luton's faint play-off hopes are still alive with the victory as they lie 10 points off fifth place, but Stockport now find themselves just two points clear of the relegation zone, with only one win in nine league matches.
VIEW FROM THE DRESSING ROOM
Luton Town manager John Still told BBC Three Counties Radio:
"He's [Steve McNulty] done fantastic. I'm really, really pleased with him - he's done very, very well, as have the back four in general. They've been solid.
"What happens when you get so many opportunities in a game and don't take them is the last 20 minutes becomes a bit anxious.
"We're not making the most of our opportunities but that's the only disappointment."