Inigo Calderon’s 67th minute red card flipped Albion’s Capital One Cup tie on its head as the Seagulls slumped to a 3-1 defeat.
Oscar Garcia’s side had been in control for much of the game, leading through Ashley Barnes’s first-half strike.
But Calderon’s dismissal for a strong, but seemingly fair, challenge on Byron Anthony – which saw the midfielder stretchered off with a suspected broken leg - inspired a comeback from the League Two new boys.
Danny Crow’s late equaliser took the game to extra time, before the striker’s magnificent finish put County 2-1 up.
Justin Edinburgh's side added a third after 102 minutes when Conor Washington rounded Casper Ankergren to knock the Seagulls out in the first round for a second consecutive season.
Albion thought they had got off to a perfect start when Jake Forster-Caskey bundled the ball home in the opening minutes, only to be foiled by the referee's whistle.
But there was nothing wrong with Barnes’s strike on 18 minutes when Rohan Ince - making his first appearance for the club – slipped in Will Buckley who in turn cut back for Barnes to guide home.
The Welsh side were not overawed though, and almost equalised through a Chris Zebrowski looping header; Tomasz Kuszczak magnificently tipping the striker’s effort over the bar.
Assistant referee Stuart Butler and County keeper Jamie Stephens both played their part in denying Albion a second. Firstly, Stephens beat away Ince’s 25-yard drive before Buckley hammered home, only to see the flag go up for offside once again.
A bright opening to the second half saw Christian Jolley force the recalled Casper Ankergren into action, with the Dane tipping away the cross-shot.
It was frantic end-to-end stuff and the visitors almost fell further behind as Barnes and Buckley combined again, but this time the former’s effort rolled just wide.
Barnes became the provider for Buckley just a minute later but the latter’s shot flashed agonisingly wide before Forster-Caskey was bundled over in the box, but no penalty was given.
Adam El-Abd is not known for his clinical streak in front of goal but the combative defender saw a spectacular half-volley from 20 yards drop just wide.
It had been a well spirited contest but on 65 minutes Calderon and Anthony went into a challenge, both full blooded, with the Newport man coming off worse.
Medics rushed onto the pitch and whilst attending to Anthony, Calderon was shown a straight red card, much to the anger of the majority inside the Amex.
After a lengthy delay, Albion were staring at the last half hour with just ten men. Vitalijs Maksimenko came on to shore up the defence but the visitors found a way through with ten minutes remaining.
A pin-point cross from Ryan Jackson was headed in off the bar by substitute Crow, much to the delight of the travelling support from South Wales.
Both sides had late chances with Adam Chapman firing wide while Barnes saw a flicked header nodded off the line.
Extra time began and Albion were dealt another blow after just four minutes as Crow curled his effort into the top corner.
Things then went from bad to worse as substitute Washington made the most of a slip in the Albion defence, rounding Ankergren before rolling the ball home.