United manager Dennis Wise and former Leeds boss Blackwell shook hands after the final whistle, but Town's head coach John Carver then stepped in and had to be restrained.
Leeds were quickly into their stride and were unfortunate not to be awarded a penalty after only seven minutes when Kandol was clipped by defender Chris Coyne a yard inside the penalty box, but referee Clive Oliver gave Coyne the benefit of the doubt, much to the Leeds crowd's disgust.
Leeds captain Alan Thompson mis-hit his shot when well placed, but it was Luton who should have opened the scoring when keeper Casper Ankergren dropped a right-wing cross and the visiting strikers failed to punish the glaring error.
Jermaine Beckford was guilty of a bad miss when Keith Keane failed to cut out Kandol's pass and Beckford missed the target when it seemed easier to score.
Leeds , however, continued to look the more impressive unit and their pressure paid off in the 44th minute when Seb Carole's pass from the left was expertly turned past goalkeeper David Forde.
It was Kandol's third goal in four games and he is starting to become a cult hero with the Leeds fans after being a scapegoat last season. He almost scored again ten minutes into the second half, shooting into the side-netting after a surging run through the Luton ranks.
Two minutes earlier Luton's Paul Furlong was denied his fourth goal of the season for a push before he turned Darren Currie's cross into the net.
And David Bell was only a whisker away from equalising with a 25-yard effort, but Leeds deservedly hung on and their deficit is now just three points.