Carlisle battled bravely with 10 men to record their first win in five home games after a moment of individual magic by Ivory Coast striker Francois Zoko.
The home side had to play with 10 men from just before the interval after Liam Noble was shown a straight red card for a late tackle on Antony Sweeney - who took no further part in the game.
Pools failed to make use of their numerical advantage and Carlisle went on to complete the win.
Noble was red carded in the 43rd minute when his late challenge left Sweeney flat out. The on-loan Sunderland youngster could have no complaints about the decision as Sweeney was helped off to be substituted by Ritchie Humphreys.
It took a special moment to break the stalemate and it was supplied by Zoko in the 67th minute when he produced an overhead kick from just outside the six-yard box to find the net after Frank Simek's cross had spun into the air off Evan Horwood.
Peter Murphy then smacked his header against the crossbar from James Berrett's corner.