With the game tied at 1-1 as the clock struck 90 minutes, substitute Kyle Cherry was fouled by Ethan Devine inside the box and Cushley kept his composure to rifle home the penalty.
After a slow opening to proceedings, the hosts would hit the front with 16 minutes on the clock. A ball into the box by Kurtis Forsythe forced Caolan Marron into scoring an own goal.
Three minutes later, the ‘Gers would go close again as Nedas Maciulaitis drifted inside the box and beat his marker, before his low effort was saved by Niall Morgan.
Dungannon Swifts boss Rodney McAree stated pre-match that Morgan would be one of the best ‘keepers in the Irish League had he elected to play soccer rather than GAA on a permanent basis.
It was hard to argue with that viewpoint as the stopper showed expert reflexes to tip Ben Tilney’s deflected effort over the crossbar.
Then, just before the half hour mark, Morgan would thwart Carrick yet again as a cross by Danny Purkis found Maciulaitis at the front post but the ex-Coleraine man was denied at close range.
After Carrick skipper Cushley was lucky to only receive a booking for a tackle on Joe Moore, the Swifts would soon grow into the game and equalised on 32 minutes.
Poor defending by the ‘Gers would be punished as Devine slipped in Moore and the speedy forward would keep his composure by slotting the ball into the back of the net.
Rodney McAree’s men would then be on the front foot as Andrew Whiteside had a long effort saved by Ross Glendinning, with Ethan McGee having a shot blocked and Devine firing the rebound wide minutes later.
In first half stoppage time, Carrick would be left frustrated yet again as a cross by Josh Andrews met the head of Curtis Allen but his looping header just went over the crossbar.
Just two minutes after the restart, the hosts thought they had regained the lead as Maciulaitis’ cross was right on the money for Purkis but his header was tipped away by the impressive Morgan.
Fox-in-the-box Allen would go close soon after as he seized upon a mistake by Marron but he was denied at close range by an alert Morgan.
However, Cushley would have the final say as he lashed home a 90th minute penalty after Cherry was brought down inside the box.
CARRICK RANGERS: Glendinning, Forsythe, Watson, Cushley (Stewart, 90+1 mins), Allen (McGuckin, 75 mins), Maciulaitis, Andrews (Cherry, 75 mins), Crowe, Reece Glendinning, Purkis, Tilney.
Subs (not used): McCauley (GK), Surgenor, Buchanan-Rolleston, O'Prey.
DUNGANNON SWIFTS: Morgan, McGee, Curry, Marron, Devine, Dillon, S. Scott (Gavlin, 90+1 mins), Glenny, Moore (Alves, 65 mins), Lusty, Whiteside (Gallagher, 65 mins)
Subs (not used): Mitchell (GK), Hegarty, Owens, Harpur.
Referee: Tony Clarke