Kyle Dempsey gave Carlisle the best possible start with an early goal, but Jed Wallace replied for Pompey and Matt Tubbs scored their second in the third minute of first half added time.
Pompey looked to have the game neatly sewn up until Wyke spotted his opening to slide the ball past Paul Jones from just inside the area.
Carlisle got off to a flying start with Dempsey’s strike inside two minutes. Brad Potts had the first effort, cutting in from the right, and when his shot was blocked Dempsey picked up possession to fire home low and right footed from 20 yards.
Portsmouth were not in it early on, but once they got their passing going they had Carlisle on the defensive and Nigel Atangana gave the home side a scare when he thundered a first time shot over the bar from just inside the area.
Pompey equalised in the 38th minute with a superb individual effort from Wallace who carried the ball forward from just inside the Carlisle half before unleashing a spectacular left-foot rocket from 25 yards that flew past Hanford and went in just under the bar for his 15th goal of the season.
Right on the stroke of half time Portsmouth went in front when Wallace turned provider, sliding a pinpoint cross across the face of goal for Tubbs to tap home from a couple of yards.
Wallace was a real thorn in Carlisle’s side and he had Hanford at full stretch to turn away a curling effort from the right hand edge of the box. Then the Pompey danger man laid on a chance for Tubbs who might have done better with the header.
Time looked to have run out for Carlisle, heading for an eleventh home defeat, when Wyke popped up for his sixth goal of the season.