Justin Edinburgh's men clinched a sixth league win from eight games at fortress Rodney Parade courtesy of efforts from Harry Worley and Conor Washington.
The win means the Exiles jump into fourth place in the table with the remaining fixture list taking place on Saturday.
The Welsh club did not look back after taking a sixth-minute lead when Robbie Willmott delivered a right-wing corner and centre-back Worley rose highest to plant his header past Scott Flinders.
Hartlepool almost drew level as Deji Oshilaja allowed the ball to run to Jack Compton, whose shot was blocked by Ismail Yakubu and James Poole's follow-up effort was routinely saved by Newport goalkeeper Lenny Pidgeley.
Moments later, the former Chelsea stopper produced a flying save to deny dangerman Poole.
Washington sealed the win in the 63rd minute with his seventh goal of the season from close range after neat work by Christian Jolley down the right flank, although Hartlepool's Andy Monkhouse hit the post in injury-time.