Heikkinen opened the scoring as he nodded home from close range in the first half.
And deadly forward Howard killed the game off with an instinctive finish from close range five minutes from time.
Both managers named unchanged line-ups for the Kenilworth Road clash and Luton burst out of the blocks.
Within four minutes they hit the post after Kevin Foley's shot had been deflected past QPR keeper Simon Royce.
It seemed to wake the visitors up and Rangers had three chances to take the lead in quick succession before the 10 minute mark.
Gareth Ainsworth fired a shot wide and Richard Langley had a free-kick well held by Hatters keeper Marlon Beresford.
Ainsworth missed the best opportunity of all after some good interplay with Marcus Bignot. He hit the ball over the bar from the edge of the area when he should have at least have tested the goalkeeper.
Luton made them pay for their misses by taking the lead on 13 minutes.
Kevin Nicholls swung over a corner and defender Heikkinen was able to steer the ball into the top corner from close range after Paul Underwood headed the ball forward.
Mike Newell's men stepped up a gear and Enoch Showunmi headed inches past the post after another corner.
Luton thought they had doubled their lead moments before half-time as Howard nodded the ball over QPR keeper Simon Royce only to eventually discover the goal had been ruled out for a foul on the keeper.
After half-time Rowan Vine had a good opening to double the lead but struck wide of the far post following a neat flick on by Howard.
Rangers raced to the other end and almost grabbed an equaliser. Paul Furlong hit a close range-shot on the turn but Beresford made a fantastic stop.
Luton substitute Warren Feeney had a goal ruled out for offside in the 67th minute just moments after coming on.
He then missed three further headed chances as the Hatters searched for a goal to kill the game off.
It arrived on 84 minutes as Carlos Edwards raced down the right and teed up Howard and the striker tucked the ball past Royce as Luton grabbed their first win of the year.