Matthew Wolfenden came off the bench after 27 minutes to help Wrexham keep their distant play-off hopes alive.
The home side had the better of the early play with Chris Smith going close, but had to reorganise when Wolfenden replaced Lamine Sakho.
After the break the substitute provided the assist for Mike Williams to stroke past Simon Rayner from six yards.
In the 82nd minute an Andrew Fleming cross was met by Wolfenden who found the bottom corner from close range.
The result provided a winning start for new Dragons chairman Ian Roberts, who took over from Geoff Moss on Friday.
It broke a seven-match unbeaten run by the Red Devils that stretched back to the beginning of December.
Wrexham manager Dean Saunders: "It was a disappointing first half, we had chances but didn't play.
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"I had a go at them at half-time - they reacted well and came out a different team. We could have gone on and scored some more.
"It was nice to see Wolfenden score his first goal for the club, he's been looking sharp for a fortnight.
"It's a great result for us, we've still got games in hand over teams and have lost once since 5 December, I think. We've got to keep it going."
Wrexham: Russell, Spann, Westwood, Assoumani, Mike Williams, Sakho (Wolfenden 27), Fleming, Smith, Holden, Baynes (Jones 76), Mangan (Gareth Taylor 72). Subs Not Used: Maxwell, Obeng.
Booked: Holden, Assoumani.
Goals: Mike Williams 59, Wolfenden 81.
Crawley Town:
Rayner, Rusk, Quinn, Broadhurst, Rents, Cogan, Hutchinson, Pinault (Napper 88), Malcolm, Smith, Killeen (Forrest 69). Subs Not Used: Jordan, Carter, Raynor.
Booked: Rusk, Killeen.
Att: 2,475
Ref: D Mohareb (Cheshire).
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