David Ross scored one goal and claimed an early assist to set Richhill on the path into the Alan Wilson Cup semi-finals.
Ross’ close-range strike kicked off the scoring before approach play alongside Andrew Allen was converted by Ally Dodds.
Lee Towers’ pass released Allen to increase the advantage to 3-0.
Neil Lester came close to adding number four before the break but his header cleared the crossbar.
However. captain Richhill managed to make his mark in the second half by steering home Richard Morrison’s corner-kick delivery.
Sunnyside cut the gap and Ross came close to adding to his tally before the final whistle.
A minute’s silence was observed prior to kick-off in memory of the Rev David Somerville.
RICHHILL: Neil McCartney, Lee Towers, Neil Lester, Kyle Davison, Mark Cooke, Lee Wortley, Richard Morrison, Johnny Allen, Andrew Allen, David Ross, Ally Dodds. Subs: Gareth Atkinson, Rhys Dougan, Gary McCoo.
Nicky Finlay and Chris Lester grabbed goals on Friday at Holm Park as Richhill Swifts shared the spoils with Keady Rovers.
Finlay was on target with a close-range finish and Lester claimed a double in the Lonsdale League draw as Rovers held a 3-1 lead.
MUFL RESERVE CHAMPIONSHIP: Rathfriland Swifts 0 Annagh United 1.
MID-ULSTER RESERVE LEAGUE DIVISION THREE: Donaghmore 2 Seagoe 0.
MID-ULSTER RESERVE LEAGUE DIVISION FOUR: Windmill Stars 2 Knockmenagh Swifts 1.
WILMOR JOHNSTON MEMORIAL CUP (ROUND TWO): Loughgall 6 Seagoe 1.
O’HARA CUP (ROUND THREE): Ballyoran 3 Silverwood United 4.