Crawley climbed into seventh place in the Blue Square Premier table after seeing off Wrexham, whose play-off hopes were dented.
Simon Weatherstone's 75th-minute shot from just inside the goal area was enough for the hosts to seal victory.
Dean Saunders' side remain in sixth place despite having failed to win in their last five games, but have games in hand on all the teams above them.
The Dragons also have games in hand over Crawley and eighth-placed Oxford.
Wrexham boss Dean Saunders: "In the first half we should have scored, we didn't have enough efforts at goal with the wind behind us.
"I thought the wind was a goal start, really and we never took advantage.
"And the actual football we played was nice, but not enough people on the end of things and not enough people having efforts at goal and to lose a game like that is just hard to swallow, really.
"But we have to bounce back from it. We were just a bit naïve."
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