Jabo Ibehre gave Carlisle an interval lead and the game burst into life in the second half after Shaun Miller was sent off for two yellow cards.
Lewis Alessandra and Padraig Amond twice levelled for Hartlepool with Danny Grainger netting Carlisle's second and Michael Raynes heading the winner.
A purposeful opening from the visitors had Carlisle on the back foot, with Lewis Hawkins and Nathan Thomas fizzing shots narrowly off target.
However, it was Carlisle who struck first in the 20th minute when a quick break down the left and a pinpoint cross from Miller provided Ibehre with a simple side-foot finish from six yards.
The home side spurned a great chance to make it two before the break when Miller seized on a loose ball just inside the area only to lash his shot over the crossbar.
Carlisle missed a double opportunity four minutes into the second half when goalkeeper Trevor Carson just managed to get a hand to Jason Kennedy's close-range effort and Ibehre ballooned the loose ball high over from four yards when it looked easier to score.
Miller, having been booked in the first half for kicking the ball away, was shown a second yellow and sent off in the 57th minute for deliberate handball.
Carlisle's 10 men were up against it in the 65th minute when Alessandra cut in from the left to power an unstoppable shot past Mark Gillespie for the equaliser.
Grainger restored Carlisle's lead three minutes later, belting a low 25-yard shot into the bottom corner after receiving a short free-kick from Nicky Adams.
Pools made it 2-2 in the 75th minute when Amond, at close range, was able to apply the finish after Gillespie had saved Billy Paynter's original drive, then Carlisle went straight back in front five minutes later when Raynes scored with a towering header from Grainger's corner.