Genaro Snijders fired the hosts into a 21st-minute lead with a goal on the break, working himself into a shooting position and drilling low into the far corner.
Rhys Oates then brought Pools level with his first goal of the season after good work by Lewis Alessandra in the 29th minute.
Parity, however, lasted just six minutes, as Lewis Hawkins fouled Carl Dickenson in the area and Graham Burke beat Adam Bartlett from the penalty spot.
In added time a melee broke out and Wes Atkinson and Toto Nsiala were sent off as a result, meaning they will miss the next group game in the competition.
The win banked County's first points in Group F as they stretched their unbeaten run to three games and, in the process, sealed their second win over Hartlepool inside a month.
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