Centre-back Paul Robinson put the Lions in front when he nodded home coolly from Chris Hackett's inswinging corner-kick.
Five minutes later it was 2-0 when Harris nipped in to capitalise on a weak header from Paul Huntington.
After 37 minutes prospects got even worse for Stockport when Harris slotted home from 15 yards after latching onto Hackett's long ball forward.
Two minutes later Harris dusted himself down after being tripped by Huntington in the box, only to see his spot-kick saved by fon Williams.
It was always going to be Harris's day though, and he slotted home his third goal from six yards in the 70th minute following some excellent work from Steve Morison.