The hosts made the perfect start when Adhamh Towe pounced on a rebound after just five minutes to fire Portadown into an early lead. The home side controlled much of the opening half, with Josh Ukek and James Teelan posing constant threats, while Rangers goalkeeper Nathan Gartside produced several key saves to keep his side in contention.
Portadown nearly extended their advantage early in the second half, but the Rangers' back line stood firm under pressure. Following a change of shape and personnel, Carrick eventually found their footing and gained momentum.
The equaliser arrived in the 79th minute when a penalty kick was awarded after midfielder Aidan Steele was brought down in the box by Eamon Fyfe, and Danny Gibson confidently slotted home.
The result leaves Carrick in 7th spot, nine points clear of Tuesday's opponents and needing just three more points from their final three fixtures to secure the position.
Carrick Rangers return to action on Saturday 11th April, when they host Ballymena United at Taylors Avenue (kick-off 15:00 GMT).