Striker McPhee was brought down by Halifax keeper Ian Dunbavin just after half-time, but he had to wait more than three minutes before he could take the successful penalty.
First Halifax midfielder Martin Foster was booked for dissent, then debutant Bertrand Cozic went down on the edge of the box claiming he had been struck by Gary Brabin.
Frenchman Cozic stayed down and needed treatment while referee Andy Page consulted an assistant over what to do.
Eventually he decided to do nothing and as Cozic walked to the touchline to cries of "cheat" from the home fans, McPhee stepped up to fire home the spot-kick.
Halifax were ahead in the fourth minute when John Grant, one of the Shaymen's most improved players, headed home Steve Haslam's cross.
Aldershot had lost both games so far and could have given up but they battled back and Halifax failed to build on their excellent start.
Dunbavin pulled off three quickfire saves from Tim Sills, Nick Crittenden and Scott Guyett, but Grant should have doubled the lead three minutes before the break.
Ryan Sugden pulled the ball back from the byline and Grant, in acres of space, slammed the ball into the side netting from close range.
Five minutes into the second half Aldershot were level and the Halifax players struggled to raise themselves.
Halifax boss Chris Wilder replaced Sugden at half-time and changed the formation to play with just Grant alone up front then, as the half wore on, he switched to three strikers.
None of those ploys worked but as Aldershot tired late on Brabin flicked on for Grant but the striker was denied by keeper Nikki Bull.
Brabin then drilled a shot just wide and in stoppage time Hassan Sulaiman cleared Brabin's header off the line.
Wilder locked his players in the dressing room at the end for an inquest into where it all went wrong in the second half.