Wrexham's Blue Square Bet Premier title bid seems over after Alfreton battled to a fifth consecutive away victory.
Anthony Wilson scored the only goal with a bullet header from Josh Law's corner on the stroke of half time.
The Dragons, who suffered their second successive home defeat, improved after the break but Jamie Tolley's effort was their only effort of note at goal.
Fleetwood will be crowned Blue Square Bet Premier champions if they win their next two games.
The second of those is at home on Tuesday to Wrexham, who trail the leaders by eight points with five games remaining.
VIEW FROM THE DRESSING ROOM
Wrexham player-manager Andy Morrell told BBC Radio Wales:
"We just weren't great today. You have to earn the right to play and we didn't do that. We kept hitting it to their strengths, which was the two centre-halves.
"We were a bit better second half a put a bit of pressure on as they sat in and tried to defend their advantage.
"They had one shot on target and scored, but we didn't create anything."
Alfreton boss Nicky Law told BBC Radio Derby:
"I think we deserved it. Late on, they knocked a lot of long balls up and we coped with that, although it did get a little bit hairy late on when they were chucking everything at it, but if I'm honest, I don't think they caused us that many problems.
"We came and played a different way today. We didn't want to come and play defensively or worry too much about them.
"I thought we'd be up against a big crowd and they'd be really up for it and they'd put us to the sword a bit, but if I'm honest, I didn't see that. I just thought we came out and I thought we coped admirably."