Neil Shaw converted a penalty kick to break the deadlock but Richhill’s response produced an equaliser off Paul Duffy’s spectacular angled volley.
Neil Lester was a threat during Richhill pressure but the game’s next talking point arrived in the favour of the Swifts.
Andrews added a physical presence to the Markethill frontline and Irwin’s measured pass released Shaw to double his personal tally with a neat finish.
Richhill’s problems increased with a red card and Mark Dickson added number three for the Swifts off an injury-time finish that featured Irwin during the build-up play.
“That now puts us on six successive wins and an unbeaten run of eight across the Intermediate B league programme,” said David Andrews, the Markethill Swifts manager. “You can see the confidence growing across the squad and I think our options on the bench made a difference last weekend against Richhill.
“Simon came on and caused problems for Richhill with his height and strength, with Kyle involved in a couple of goals.
“We also used Ian McCracken so that was pleasing to see our substitutes come on and be able to help the team.
“Having Ryan McElroy, Simon and Michael Dobbs back at the club has been another boost this season.
“We do not have that different a squad compared to last season and everyone is delighted at the run of form.”
MARKETHILL SWIFTS: Aaron Dickson, Matt Black, Karl Wilson, Scott Cully, Ryan McMahon, Adam Cooke, Michael Dobbs, Mark Dickson, Ryan McElroy, Neil Shaw, Jordan Stephens. Subs: Simon Andrews, Kyle Irwin, Ian McCracken.