Charles Ademeno scored a hat-trick in the first six minutes as Crawley heaped more misery on struggling Grays.
Ademeno fired the visitors into the lead after latching on to Callum Willock's pass and then doubled their advantage from close range.
Another tap-in gave Ademeno his hat-trick, with just four minutes and two seconds separating his three goals.
A Jake Reid penalty and a Folawiyo Onibuje header made it 3-2 before half-time but they could not equalise.
Grays Athletic manager Julian Dicks told BBC Essex:
"Three goals in six minutes is just not acceptable.
"When we went three down our character showed through and we got a couple of goals.
"But in the second-half we didn't do enough to win it."
Crawley Town manager Steve Evans told BBC Surrey:
"We had to be quite defensive minded in the second-half and play with a little bit of caution.
"I cannot fault my players. We've come away from home, we've got a good win and taken four out of six points in the festive period.
"We have one more (game) to come, and dare I say it if we'd been offered seven out of nine points after these games then we'd have snapped their hand off."
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