Lancashire-based official Leake awarded Peterborough a hotly-disputed spot-kick in the third minute of first-half stoppage time to give the visitors the chance of an equaliser.
Leake blew for Efe Sodje's slight tug on Clive Platt's shirt despite having waved away appeals for a penalty seconds earlier when Huddersfield's Chris Brandon blatantly handled in the box.
There was some confusion about what exactly had been given with both sets of fans as puzzled as the players.
Most of Posh's own team believed the referee had given a free-kick to the home side and to compound the error video replays showed there was virtually no contact between Sodje and Platt as the pair challenged for Danny Sonner's corner.
When the chaos eventually died down Peterborough captain Curtis Woodhouse crashed the penalty home to level the scores.
Earlier McAliskey had given Huddersfield the lead at the second attempt from close range after latching on to Robert Edwards' byline cross.
And despite the blow of conceding an equaliser in such controversial circumstances just before half time, Huddersfield went on to win the match thanks to the vision of striker Pawel Abbott.
Former Poland under-21 international Abbott split United's defence with a diagonal through ball that left Jon Worthington clear.
Midfielder Worthington raced in on goal unchallenged and tucked a low shot underneath keeper Mark Tyler after 48 minutes.
The home side had further chances to extend the lead with both McAliskey and Abbott testing Tyler in the closing stages.
But it was yet again the referee who had the last word when he denied Huddersfield a certain penalty after 59 minutes.
Abbott exchanged passes with McAliskey on the edge of the box and surged into the danger area only to be chopped down from behind by Craig Ireland's cynical foul.
But unimpressed Mr Leake waved play on much to the disgust of the home players and fans.