Manager Justin Edinburgh hailed Newport's 3-2 victory over Chesterfield on Sunday as their best of the season.
The Welsh club, promoted from the Conference last season, appeared on the ropes after Jimmy Ryan had cancelled out Danny Crow's earlier effort.
But Liam Cooper hauled down Conor Washington in the penalty area, resulting in his dismissal, and Adam Chapman duly fired home from the spot.
Andy Sandell then completed the job before fellow substitute Marc Richards claimed an injury-time consolation to set up a frantic finale, but County held on to climb up to eighth in the League Two table, just two points behind the second-placed Spireites.
Edinburgh said: "It's the best win of our season there's no doubt about that. It's a hugely pleasing result.
"The progress we have made as a football club is fantastic and this group of players are really beginning to believe they can compete in this division.
"They're the best team in the league but we competed with them and got the result.
"You have to give credit to the opposition, they came out and shut us down in the second half but we weathered the storm and showed great spirit and belief.
"The penalty was the linesman's decision but there's no doubt it was the correct one.
"You have to make your own luck and Conor's run did that. He is growing all the time. He's a great prospect; a good lad, and will only get better.
"We're disappointed to concede the goals, it's never nice to give them away especially after five clean sheets but we also scored three having not scored for a while."