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."