Mickey Demetriou's last-minute header earned County back-to-back league wins for the first time since August.
With the clock ticking down, Demetriou leapt highest to power home a cross from the right to send the 95 travelling Exiles into delirium behind the goal.
After having the better of the play for much of the afternoon, County piled on the pressure in the final 10 minutes after Rory Feely was shown a straight red card for his foul on Adam Lewis in the 80th minute.
County thought they had the start of their wildest dreams when former Bluebird Offrande Zanzala slotted home within the first minute after Charlie McNeill and Adam Lewis combined to set-up Zanzala.
However, as Newport wheeled away to celebrate, the flag went up for offside and the early joy was wiped out.
Ged Garner had Barrow's first chance of the contest just after the quarter-hour mark as his diving header caused Nick Townsend trouble, but County's keeper made a great diving save to his right to catch it.
Barrow went close again soon after, but Sam McClelland flicked over the bar from inside the area after a cross from the right.
Ben Whitfield then had a go on the turn inside the box, but that was straight at Townsend and easily caught.
Barrow went close 12 minutes into the second half as Elliot Newby progressed towards goal before having his shot from the right of the box deflected behind for a corner.
That corner only led to another one, with McClelland headed wide after it was swung in from the right.
Newport went straight down the other end though but Aaron Lewis struck narrowly wide from a tight angle. The men in grey were convinced Farman got a hand to it, but goal-kick was given.
County came close again three minutes later and only a terrific sliding block denied Zanzala's shot as he tried to test Farman in the Barrow goal.
Graham Coughlan's side really put the pressure on in the final 20 minutes, with Adam Lewis having a go first with an ambitious shot from range that went harmlessly wide.
Mickey Demetriou had the same fate soon after, also striking wide from distance.
Second-half sub Omar Bogle then had a good effort from the D that curled into the arms of Farman who did well to grab it.
Farman was then needed to make a top drawer save to dive to his left to push away a great header by Calum Kavanagh after Cameron Norman's ball in from the right.
Barrow were then reduced to 10 after that Feely red card and Newport kept pushing for that winner.
Kavanagh had another opportunity to make it two goals in two County appearances, but he was unlucky to get the ball stuck under his foot after he tried to connect to Norman's shot with a slide at goal.
The three points went County's way eventually though thanks to Demetriou's last-gasp winner.
Barrow: Paul Farman, Patrick Brough, Sam McClelland, Niall Canavan (C), Elliot Newby (Jake Young '75), Billy Waters (Tyrell Warren '83), Tom White (Sam Foley '86), Harrison Neal (Robbie Gotts '75), Ged Garner (Richie Bennett '75), Rory Feely, Ben Whitfield
Subs not used: Josh Lillis
Newport County: Nick Townsend, James Clarke, Priestley Farquharson, Mickey Demetriou (C), Cameron Norman, Adam Lewis, Scot Bennett, Aaron Lewis, Harry Charsley (Will Evans '88), Charlie McNeill (Calum Kavanagh '63), Offrande Zanzala (Omar Bogle '63)
Subs not used: Joe Day, Matt Baker, Nathan Moriah-Welsh, James Waite