A last-minute equaliser from Lee Noble secured a point for in-form Dartford.
Danny Harris gave the visitors a fourth-minute lead with a shot from the edge of the area.
Wrexham soon levelled as Danny Wright drilled into the top left corner after finding a yard in a crowded area.
The home side took the lead on the stroke of half-time when Andy Bishop lifted the ball into the net, but late Dartford pressure was converted when Noble struck with a 25-yard free-kick.
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Wrexham player-manager Andy Morrell told BBC Radio Wales:
"Our shape was all over the place. It could have been 6-6. We probably should have had a penalty but I don't think we deserved to win.
"We've got to re-group and be better. I think we were lucky to get away with a draw in the end.
"They had chances, and I know we had chances to put it to bed but we weren't clinical enough in the box. We were way off where we expect the lads to be."
Dartford manager Tony Burman told BBC Sport:
"I'm delighted with the result, especially with the second-half performance.
"I thought we thoroughly deserved what we got out of the game. When it was 1-1 we had chances and we got punished.
"We've come to a fantastic place, lots of history, good side, experienced side, and I think we've come here and given a good account of ourselves.
"We've been a big club in lower leagues and teams come and play a certain way, and I think Wrexham found our counter0-attacks dangerous."