It was the Swifts who started the brightest, aided by the wind, Andrew Mitchell first blazing past the post before the Swifts won a string of corners. The 'Gers were resolute in defence and kept the game scoreless.
Carrick then took the lead, a free-kick hung in the wind allowing Joe Crowe to win the header and then play a one-two with Adam Lecky before he slotted across goal and passed Declan Dunne.
Carrick continued to dominate and doubled their advantage soon after. Michael Place maintained his impressive form since joining the club, floating a perfectly weighted cross in behind the defence from the right flank and Paul Heatley timed his run to perfection and calmly slotted home to make it 2–0.
The hosts were in full flow and extended their lead midway through the first half. Danny Gibson surged down the right-wing to the byline before cutting the ball across the six-yard box. The delivery evaded Dunne and fell kindly to Lecky, who made no mistake from close range.
While the second half proved more unsettled, Rangers effectively sealed the contest just after the hour mark. Place swung in a dangerous corner and, following a scramble in the box, Lecky reacted quickest to poke the ball home from close range for his second of the afternoon.
Dungannon briefly reduced the deficit when Liggett headed home from five yards, but any hopes of a comeback were swiftly extinguished. Just two minutes later, Lecky completed a superb hat-trick - racing onto a long ball forward, beating the offside trap and calmly tucking a low finish beyond Dunne to round off an outstanding team display.
The victory sees Carrick Rangers climb above Crusaders and Ballymena United into ninth place in the league table.
The in-form Amber Army now turn their attention to a trip to Portadown at Shamrock Park on Saturday 31 January (17:30 GMT), where another positive result would see Rangers overtake the Ports in the standings.