Dungannon made an early breakthrough when Cathal McGinty turned in from close range after just three minutes, following a corner. Carrick then suffered an early setback when Joe Crowe was forced off injured, but his replacement Aidan Steele made an immediate impact, setting up Danny Gibson to level the game in the 37th minute.
The Swifts regained the lead early in the second half after a penalty was awarded when goalkeeper Nathan Gartside collided with Danny Wallace while collecting a loose ball. McAllister converted from the spot to restore Dungannon’s advantage.
Carrick responded with resilience and were unfortunate not to be awarded a goal when Aidan Steele’s effort appeared to cross the line, but the officials were unmoved. Paul Heatley did draw the home side level in the 76th minute, heading home from a Gibson delivery to the edge of the six-yard box. Three minutes later, Steele capped an impressive cameo by driving through two defenders and firing Carrick ahead.
However, Dungannon salvaged a point late on when McAllister met a deep cross to score his second goal of the match in stoppage time.
Despite the late disappointment, Carrick again impressed against a top-half side and could feel aggrieved not to take maximum points. Manager Stephen Baxter praised his side’s performance, highlighting Steele’s influence after his early introduction and their control of large periods of the second half in difficult wind conditions.
The 'Gers travel to Ballymena United next on Saturday, 20 December, with just three points separating the sides. Kick-off is at 15:00 GMT, with live coverage available to subscribers outside the UK on OneFootball.