Barrow are two points adrift of safety after Richie Baker's penalty earned them victory at Dartford.
Danny Harris went close for the hosts when his shot from the right flew wide, while Adam Boyes almost put Barrow ahead with a 20-yard strike.
Richard Rose fouled Alex-Ray Harvey in the area and Baker converted the spot-kick to score the winner.
The Darts could have levelled late on but Tom Champion's header was too close to Barrow keeper Danny Hurst.
VIEW FROM THE DRESSING ROOM
Dartford manager Tony Burman told BBC Radio Kent:
"I thought we deserved something out of the game. The lads got back to a good work rate and effort.
"It's disappointing, we weren't torn apart. It's a penalty they were given and if we had more quality in the final third maybe things would have changed.
"Three decisions have gone against us and it does change the game. Disappointed to lose but I'm not going to fault the effort after Saturday."