Billy Bingham's strike secured Dagenham their place in League Two and dented Crawley's push for automatic promotion.
It was the visitors who took the lead when Charlie Wassmer turned in Scott Davies' low cross.
They should have made it 2-0 just before the break, but Gary Alexander scuffed his volley wide.
Bingham drew Daggers level in spectacular fashion when he picked up the ball midway inside the Crawley half and blasted it home from 30 yards.
After the break, Davies again found Alexander in space but he powered his shot over the bar.
Abu Ogogo had the final chance of the match to snatch three points but the Daggers man shot wide from the edge of the box.
Crawley remain third in the table, a point inside the automatic promotion places.
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Crawley caretaker manager Craig Brewster told BBC Sussex:
"I don't think we did enough to win the game, albeit we had two fantastic chances.
"You've got to give credit to Dagenham, they worked hard. But when they score a 30-yard strike in the 46th minute of the first half, sometimes you have to take your hat off to the boy.
"But you look at the scores around us, and it could be a big point."
Dag & Red 30 Lewington 04 Doe 06 Arber 36 Baudry 41 Spillane 03 McCrory 12 Elito 19 Ogogo 24 Bingham 10 Scott (Green - 83' ) 23 Woodall Substitutes 27 Hogan 17 Howell 18 Parker 37 Green 14 Reed Crawley Town 01 Kuipers 03 Howell 05 McFadzean Booked 20 Wassmer 28 Davis 02 Davies 07 Clarke 11 Simpson 15 Bulman 22 Neilson (Akinde - 75' ) 09 Alexander Substitutes 25 Shearer 18 Dempster 13 Hunt 10 Watt 17 Akinde
Ref: Danny McDermid