Darlington substitute Greg Blundell struck in the last minute to give his side their second away win this season and leave Luton stranded at the bottom.
Billy Clarke had put the visitors ahead when he touched in Rob Purdie's free-kick at the near post.
Claude Gnakpa powerfully headed in Rossi Jarvis's free-kick to equalise with his first goal for the Hatters.
Purdie hit Luton's bar before Blundell fired into the roof of the net and Asa Hall then hit the bar at the other end.
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