In freezing conditions, both sides did their best to provide an entertaining encounter but time after time their efforts were frustrated by over zealous referee, who awarded more than 40 free-kicks and showed a total of seven yellow cards in a game that contained no serious foul play.
The home side got off to a perfect start after going in front within the first two minutes.
A quickly-taken Adam Le Fondre free-kick released over-lapping full-back Scott Wiseman and his pin-point low cross was headed home at the near post by a diving Lee Thorpe.
The home side should have doubled their lead eight minutes later when teenager Will Buckley and captain Gary Jones combined to send Thorpe through on goal but, as Luton keeper Conrad Logan raced out to meet him, the veteran striker fired over.
Rochdale doubled their lead 13 minutes after the break when referee Bratt pointed to the spot following a foul on defender Rory McArdle as he tried to get on the end of a Tom Kennedy corner.
After the usual fruitless arguments had died down, Le Fondre calmly sent Logan the wrong way for his fourth goal of the week.
Le Fondre might have stretched Dale's lead in the 75th minute after good work by Thorpe but his effort from the edge of the box went narrowly over.
The only chance created by the visitors came after 77 minutes when substitute Drew Talbot saw his downward header brilliantly saved by home keeper Sam Russell to ensure a first clean sheet since the season's opening day at Grimsby.