Rovers will face Oxford United in the fourth round of the Emirates FA Cup after edging a dramatic cup-tie at Rodney Parade.
Ben Marshall fired Rovers in front from the spot after just 8 minutes, but the Lancashire club then found themselves a man down after Chris Brown was given his marching orders for a foul on Medy Elito meaning they'd have to play more than 80 minutes with ten men.
County captain Mark Byrne made that advantage count when he put the hosts level in emphatic fashion just past the half hour, before Conor Dymond struck the post as Newport ended the first half strongly.
But the introduction of Jordan Rhodes at the start of the second half saw Rovers come out and control the game, eventually getting their reward on 75 minutes when the striker glanced home Tom Lawrence's cross.
Scott Boden missed a great chance to put the Exiles back on level terms in the closing stages, but as keeper Joe Day was red-carded for a late lunge on Craig Conway, Rovers saw out the remaining seconds to secure a match with Oxford at the Kassam Stadium.
Before kick-off Rovers had named six substitutes with Matt Kilgallon missing out due to illness, and that number was reduced to five by the the time the game got underway as Lee Williamson picked up a calf strain in the warm-up, Elliott Bennett taking his place.
Jason Steele was called into action early doors to claim a dangerous ball in from the left, before Rovers threatened through Chris Brown.
Tommy Spurr made space down the left flank to send over a low centre that Brown stooped to head but the ball flashed narrowly over the bar.
Chris Taylor, one of Rovers' cup heroes from last season, then laid on the key pass that saw the Lancashire club open the scoring from the penalty spot on 8 minutes. Collecting a ball from Ben Marshall he returned it to the defender and he danced into the area only to be upended by Scott Barrow.
Referee Charles Breakspear pointed to the spot and Marshall made no mistake from 12-yards, his shot finding the bottom right corner of the goal.
But no sooner had Rovers taken the lead they were reduced to ten men.
A mis-timed challenge from Brown on Medy Elito saw the County midfielder down and in some pain. But Breakspear stunned the Rovers striker by issuing him a straight red card. Elito played no further part as he was stretchered off to be replaced by Tom Owen-Evans.
Urged on by a vociferous home support, Steele had to show good acrobatics to tip over a long-range effort from Exiles captain Mark Byrne.
Whilst at the other end a clever pass from Marshall saw Hope Akpan race into the area but his cut-back was headed over by a diving Taylor.
After going close earlier in the half from distance, midfielder Byrne then put the hosts back on level terms with a stunning strike on 31 minutes.
Collecting a pass in the centre of the park, Byrne let fly from 25-yards, giving Steele no chance as the ball flew into the top-right corner.
County then went close to grabbing a half-time lead thanks to Conor Dymond's clever flick, the ball grazing the outside of the post.
But after being shell-shocked for the majority of the half, Rovers regained some composure in the closing stages, however they were unable to threaten the home goal further.
Jordan Rhodes was introduced at the start of the second half, replacing Bennett. He joined Tom Lawrence up front in a 4-3-2 formation and ten minutes in the striker would go close, getting his head to a Tommy Spurr corner, but the ball flashed wide of the mark.
Rhodes then saw an effort on the turn blocked, Lawrence like-wise, before Taylor let fly only to see his shot deflect behind. Moments later the three combined again on the edge of the Newport box but Lawrence was well off target.
Rovers continued to force the pace, Taylor blazed over after a neat knockdown by Rhodes, before an exchange of pass between Corry Evans and Lawrence saw the ball run through to Rhodes but his shot on the turn was wide.
But after continuing to knock on the door, eventually Rovers grabbed a second goal their their second half play deserved on 75.
Following a foul on Spurr, Lawrence saw his initial free-kick cleared only as far as Evans, his clever pass found Lawrence once more and this time his delivery found it's intended target as Rhodes escaped his marker to nod home his tenth goal of the season.
But despite Rovers dominating for long spells in the second period, the home side should have levelled with nine minutes to go.
Aaron Collins sent a teasing ball in from the right to where Scott Boden was unmarked six-yards out, but inexplicably he headed over Steele's bar.
That could have prompted a lively end to the match but to their credit Rovers showed a calmness and a maturity under pressure in the closing stages and in the end both sides finished with ten men as County keeper Joe Day saw red for bringing down substitute Craig Conway in the final moments.
The result sees last season's quarter-finalists reach round four and an away trip to take on Oxford United at the end of the month.
NEWPORT: Day, Hughes, Donacien, Holmes, Barrow (sub Green 90+6 mins), Byrne (c), Dymond (sub Taylor 82 mins), Elito (sub Owen-Evans 14 mins), Boden, Collins, Davies.
Subs not used: Parselle, Twumasi, Ralph, Klukowski
Goals: Byrne 31 mins
ROVERS: Steele, Marshall, Hanley, Lenihan, Spurr, Bennett (sub Rhodes 46 mins), Evans (sub Henley 90 mins), Akpan, Taylor, Lawrence (sub Conway 77 mins), Brown.
Subs not used: Raya (GK), Olsson.
Goals: Marshall (pen) 8 mins, Rhodes 75 mins.
Booked: Lawrence, Taylor.
Attendance: 5083 (including 558 Rovers fans)