Own goals from Danny Swailes and Paul Huntington plus strikes from Steve Morison, Schofield and Jonathan Obika made it a miserable day for basement boys County.
The Lions pummelled the visitors' goal early on but a moment of madness from Swailes gifted the hosts the lead when, under no pressure, the defender headed Chris Hackett's 27th-minute free-kick past his own goalkeeper.
Other than Jemal Johnson stinging David Forde's hands from distance, County offered little response while Harris rattled the crossbar as the Lions looked to turn the screw.
The inevitable second came when Tony Craig's corner was squeezed in at the far post by Steve Morison after 42 minutes, and Schofield raced through to round the goalkeeper and make it three on the stroke of half-time.
Schofield was the architect for the fourth when his jinking run and cross was turned into his own net by Huntington after 58 minutes, before substitute Obika swept home in the 69th minute to complete the rout.