Carlisle worked hard but came away with nothing as Newport overturned a sluggish start to take the points on a cold day in South Wales.
Newport started confidently as they took the game to their visitors but United held their shape to keep the probing at bay.
United had an opportunity to mount an attack of their own when Dempsey whipped a deep free kick into the box. Day watched it into his hands as it skipped up off the greasy surface.
Patient build-up play almost brought reward for the Cumbrians when Asamoah shielded it wide on the right. Potts took over and his drilled cross was just in front of Dempsey as he lurked in the area.
A long kick from Hanford caused panic at the back as Yakubu struggled to deal with it and his weak clearance brought a shot on the spin from Asamoah. Yakubu was off balance but he did enough to send it behind for a corner. Dempsey whisked that one into the mix and Meppen-Walter bagged his second goal for the club when he thundered an unstoppable header into the bottom corner.
It was suddenly all about Carlisle and Day had to keep a close eye on a Dempsey shot as it skipped off the bumpy surface and into his hands. Potts was next to go close when he pulled wide in support of Sweeney and a rolled pass invited the shot. The keeper had to go full length to tip it away.
Captain Danny Grainger went for the spectacular and the unexpected when he spotted Day edging off his line midway through the half. An accurate, dipping shot from five yards inside his own half followed and the stopper did well to back track and palm it over the bar.
Archibald-Henville put a diving header wide from that delivery and both Sweeney and Asamoah dragged shots across the face of goal as the Cumbrians continued to dominate the play.
The blue shirts weren't shy when it came to shooting and Potts had Day on his toes once again with another firm effort which had to be gathered at the first attempt.
Newport came into the game just before the half hour when a cross to the far post sat up nicely for Minshull. He opted for power and was disappointed to see it rise high over the bar.
County looked like a team starting to settle and they should have been back on terms when Byrne beat the wall with a 24 yard free kick. Hanford pushed it onto the post and O'Connor was guilty of a glaring miss when he somehow popped the rebound wide from just a yard out.
Keeper Hanford earned pats on the back all round moments later when Zebroski was left unmarked to race onto a Sandell cross. His header had power and accuracy but a block on the line was followed by a welcome clearance from Anderson.
The action switched to the other end and Day had to make sure as Grainger tried to slot the ball into his near post, when the keeper struggled to keep his lines of sight clear at a 25 yard free kick.
Newport grabbed their equaliser on the stroke of half time when Jackson wound his way off the touchline and into the box. Grainger appeared to pull him back and the referee had no hesitation in pointing to the spot. Adam Chapman placed it and sent Hanford the wrong way with a well taken finish.
County enjoyed the bulk of the possession after the break but a succession of crosses were dealt with as Jackson and Zebroski provided the deliveries.
It wasn't all one way traffic though and Potts had a shot blocked following good build up play on the right, with Asamoah and Dempsey involved.
United were incisive when a long ball forward from Meppen-Walter was flicked on for Potts to chase. Dempsey pulled into space but he was off balance as he sent a shot into the stands.
Newport responded with a neat attack of their own when Chapman was given time to cross. O'connor was unmarked but he couldn't keep his header on target.
That sparked a better spell for the hosts and they took the lead when a great save from the feet of Hanford rebounded favourably into Minshull's path. He kept his head over the ball and sent a rasper into the top corner.
County closed ranks as they reshaped to hold onto their lead and they almost added another when Howe found Byrne on the edge of the area. He drilled one just wide of the upright as the home fans got themselves ready to celebrate their hard earned three points.
Newport - Chapman (44 pen), Minshull (70)
United - Meppen-Walter (11)
Newport - Byrne (37)
United - Grainger (44), Robson (82)
Newport County - Day, Jackson, Poole, Jones, Yakubu, Sandell, Chapman, Byrne (Porter 86), Minshull, O'Connor (Jeffers 90), Zebroski (Howe 71). Subs - Stephens, Flynn, Klukowski, Collins.
Carlisle United - Hanford, Brown, Archibald-Henville, Anderson, Grainger, Thirlwell (Robson 75), Meppen-Walter (Rigg 82), Potts, Sweeney, Dempsey, Asamoah (Beck 71). Subs - Gillespie, Amoo, Brough, Symington.
Referee - Mr Darren Sheldrake
Attendance - 3,273 (216 away fans)