Stanley picked up their first point of the season in an exciting draw at the Store First Stadium.
The Reds raced into a two-goal lead before Luton came back to level the scores before half-time.
Stanley could have won it in injury-time with Rob Atkinson having a header cleared off the line but they had to settle for a point.
James Beattie’s side got off to a dream start when they opened the scoring on nine minutes. George Bowerman got the ball in midfield, found Piero Mingoia who raced down the left wing and played in a cross with James Gray sliding the ball home.
And it was two on 16 minutes when a Mingoia corner was only half cleared to Luke Joyce on the edge of the area. The captain headed goalwards and the ball bounced off the post and into the net.
Luton boss John Still made an early substitution, bringing off midfielder Alex Lacey and replacing him with Luke Guttridge on 23 minutes.
The change benefited the Hatters and they were back in the game on 31 minutes when Luke Rooney curled the ball into the far corner of the net.
And Luton were level on 42 minutes when they won a disputed free kick on the edge of the area. Jake Howells took it and it got a deflection, wrong-footing debutant keeper Jay Lynch.
The game was wide open in the second half and it went from end to end. Keeper Lynch kept out strikes from Guttridge and Paul Benson while Tyler tipped over a Gray blast in injury time.
From the resulting corner, defender Atkinson had a header cleared off the line as they had to settle for a point.