Hale latched onto a wayward pass from goalkeeper McIntyre before curling a shot from outside the box into the bottom-right corner.
The Reds extended their lead in the second half through Parsons, who was marking his first start after arriving in January from Brisbane Roar.
After Reece Webb was dispossessed, Parsons charged into the box and unleashed a ferocious drive at the near post, catching McIntyre off guard.
The home side capped a professional performance with a late third, when the visitors failed to clear their lines late on, allowing McGuinness to rifle into the top corner.
Despite a spirited effort, Carrick lacked precision in front of goal. Danny Gibson came closest in the first half, smashing a powerful shot off the near post, while Adam Foley's glancing header late on narrowly missed the mark.
Kyle Cherry thought he'd got his side back into the game, but his close-range effort was ruled out, with neither Jamie Robinson nor his assistant deeming the ball had crossed the line.
Next up for the Reds is a trip to face Glenavon while Stephen Baxter's men make the journey to Stangmore Park.