The Reds, bottom of League Two the start of play, opened the scoring on nine minutes when Piero Mingoia raced down the left flank and played in a cross for James Gray to fire in.
And it was two on 16 minutes when a Mingoia corner was only half cleared to Luke Joyce and, when the captain headed goalwards, the ball bounced off the post, hit keeper Mark Tyler and dropped in.
Luton boss John Still made an early substitution, bringing off midfielder Alex Lacey and replacing him with Luke Guttridge on 23 minutes and he fired just wide with almost his first touch.
The change benefited the Hatters and they were back in the game on 31 minutes when Luke Rooney got into the area, created space and curled the ball into the far corner of the net.
And Luton were level on 42 minutes when Luke Howells' free kick on the edge of the area took a deflection and found the corner, wrong-footing debutant keeper Jay Lynch.
The game was wide open in the second half, with Lynch denying Guttridge and Paul Benson.
Tyler tipped over a Gray blast in injury time while Rob Atkinson's header was cleared off the line at the death.