Justin Edinburgh's side are riding high in fourth ahead of the weekend fixtures and hit the front when Harry Worley headed home Robbie Willmott's cross with seven minutes on the clock.
County striker Conor Washington notched his seventh goal of the season from close range after 64 minutes to give the hosts breathing space.
Hartlepool's main threat came via forward James Poole, who was twice denied by Lenny Pidgeley in the Newport goal.
Newport have now won their last five matches at Rodney Parade in all competitions, while 13th-placed Hartlepool could not make it six wins from seven league outings and have now lost back-to-back games on their travels.
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