Simon Weaver's team were without a League Two win on home turf since they overcame Barrow on October 17, but a timely three-point haul opens up a significant gap between themselves and the relegation zone.
And a deserved victory it was too, with the Sulphurites rewarded for a far more positive performance than anything served up at the EnviroVent Stadium in months.
The early exchanges were fairly even, Town's Ed Francis coming closest to breaking the deadlock when he curled a left-footed free-kick narrowly wide of the post with Exiles custodian Nick Townsend scrambling.
It was however the visitors who drew first blood, from a goal out of nothing following all-too-familiar failings inside the Harrogate box.
After conceding twice in the space of as many minutes from corners during their midweek loss at Tranmere Rovers, the Sulphurites were again undone at a set-piece on 17 minutes.
Matty Dolan's left-wing delivery wasn't dealt with initially and the ball broke for Luke Gambin, whose blast from the edge of the area was deflected past James Belshaw by Jake Scrimshaw.
Having drawn a blank in each of their previous three home fixtures, Town passed up a glorious chance to equalise six minutes after falling behind, Josh McPake failing to beat Townsend after March played him through on the Exiles' goal.
But that miss was quickly forgotten as Weaver's men registered what was their first goal at Wetherby Road in around 320 minutes of football.
Belshaw's free-kick from deep inside his own half was flicked on superbly by Martin for strike partner March to run in behind and send a clinical finish across Townsend and into the far corner of the net.
Almost straight from the re-start, Scrimshaw drilled a strike narrowly past the post as County looked for an immediate response, though the opening half finished with the hosts on top and wondering why Simon Power was not awarded a penalty by referee Chris Pollard after being brought down inside the box.
The second period began with Town very much on the front foot and McPake causing the visitors real problems with his dancing feet down the left wing.
From the opposite side of the pitch, Power then rolled the ball across the goal-line however both March at the near post, then Martin behind him failed to apply a finishing touch.
A lovely one-two between Power and March then led to the former seeing an effort blocked, before George Thomson had a strike spectacularly pushed away by Townsend in the Newport goal.
With the Exiles defending desperately in an attempt to repel wave after wave of Harrogate attacks, a second home goal looked on the cards and duly arrived on 66 minutes.
Thomson sent over an inviting left-wing corner which Martin met with his head inside the six-yard-box and powered home to register his first league strike since September.
The hosts kept coming, showing real intent to take the game out of County's reach and were then boosted further when Liam Shephard was sent-off for a lunge that was undoubtedly two-footed, but certainly didn't make contact with an opposition player.
The 10 men actually looked more likely to get back in the game than Newport's full compliment had, and almost did so in the final minute of normal time.
Belshaw came a long way off his line to claim a ball into the box that he was never getting to, presenting Ryan Taylor with a clear sight of goal, though Jake Lawlor was perfectly positioned to effect a crucial goal-line clearance with his head.
Harrogate remain 20th in League Two despite their victory, but now sit nine points clear of the bottom two with a game in hand on both of the sides currently occupying the drop zone.
Harrogate Town: Belshaw; Burrell, Lawlor, Smith, Francis; Power, Thomson, Falkingham, McPake; March, Martin (Muldoon 85). Unused substitutes: Minter, Hondermarck, Kiernan, Kerry, Williams.
Newport County: Townsend; Shephard, Longe-King, Dolan (Wilmott 62), Demetriou, Haynes; Gambin (Amond 76), Bennett, Hartigan (Collins 88); Taylor, Scrimshaw (Telford 62). Unused substitutes: King, Baker, Evans.
Referee: C Pollard.