Richhill entered the Alan Wilson Cup tie off the back of six successive league wins - but Bourneview Mill had cause to cheer at the close of play.
Gary Hill hit home a superb hat-trick at Pepperton Park - with Stephen Elliott the other home scorer.
A strong start by the Mill featured early efforts for Kyle Abraham and Hill before the latter headed home Elliott’s cross after good work by Jeff McClure.
Hill then raced clear of the offside trap and found the net with a measured lob.
His free-kick finish into the top corner wrapped up a slick treble - with Tom McClelland and Mark Boyce both hitting the frame of the goal.
Captain Robert Dodds proved the pick of the Richhill players.
BOURNEVIEW MILL: Andrew Neill, Jeff McClure, Tom McClelland, Ross McDonald, Dale Compton, Stephen Elliott, Gary Hill, Andrew Weir, Mark Boyce, Geoff Neill, Kyle Abraham. Subs: Andrew Topley, Dean Currie, Dave Stewart.