Andy Brown's header on the stroke of half-time moved Nuneaton off the bottom of the league table with a victory over play-off hopefuls Dartford.
Danny Newton and Connor Taylor went close for the hosts, before Brown converted Neil Cartwright's cross for the only goal of the game.
Dartford's Harry Crawford put his header over the bar, while Jon Wallis had also squandered a chance to level.
Nuneaton are now only three points adrift of safety.
Dartford remain in the Blue Square Bet Premier play-off positions on goal difference ahead of sixth-placed Luton Town, although the Hatters have two games in hand.
VIEW FROM THE DRESSING ROOM
Dartford manager Tony Burman told BBC Radio Kent:
"I can't say it's one of the best performances we've had but fair play to Nuneaton. They've battled away and we tried to make things too difficult.
"I hate to concede from a set piece when it's 46 minutes and somebody makes a stupid challenge.
"We should have had a stonewall penalty without any shadow of a doubt but please don't hide the fact that we put in a poor shift and that's not acceptable."
Nuneaton 23 Smith 02 Cartwright 05 Dean 14 Forsdick Booked 15 Gordon 18 James (York - 62' ) 21 O'Halloran 06 Walker Booked 10 Brown 17 Newton 26 Taylor Substitutes 11 Adams 12 Armson 13 Sleath 07 York 20 Thompson-Brown Dartford 12 Bettinelli 02 Rose 04 Champion 05 Ajayi 13 Rogers 08 Wallis 14 Noble (Collier - 78' Booked ) 20 Burns 07 Hayes (Crawford - 54' ) 09 Erskine 11 Harris Substitutes 24 Sutton 03 Green 15 Collier 26 Monger 21 Crawford