Harry Charsley's first goal in Newport amber was not enough, as promotion chasing Salford got the win at the Peninsula Stadium.
County did take the lead in the 29th minute when January signing Harry Charsley made it 1-0 with his first goal for the club, but two goals either side of the half-time whistle turned the game around for the Ammies.
Callum Hendry levelled the contest as the game entered the 45th minute, and then first-half sub Conor McAleny struck in the opening minute of the second half for 2-1.
Matt Smith finalised matters in second-half stoppage time with a header from a corner.
Salford did start the game on top, with the first effort on goal being Ethan Galbraith's attempt from distance after three minutes that Joe Day did well to smother with a dive to his right.
Day was also needed a minute later to deny Ibou Touray to keep out Salford's early intent.
The game slowed down after that, until Omar Bogle had a shot brilliantly saved by Alex Cairns in the Salford goal, but a free-kick had already been whistled for after a foul in the build-up to the chance.
County then struck seven minutes later, with Charsley finishing low into the bottom left corner after finding plenty of space in the box following a pass from Priestley Farquharson.
Bogle almost scored an absolutely lovely goal soon after, but his delicate little bink was palmed wide by Cairns after Bogle was found by Charlie McNeill. Puzzingly a goal-kick was given, however.
Day was then needed to make his first excellent save in quick succession, as he was somehow able to tip Louie Barry's header from point-blank range onto the bar and away.
Before that second save though, Bogle had a strike from distance held by Cairns, who did well to avoid a nasty bobble off the tired turf at the Peninsula.
McAleny was then denied by a brilliant low diving save to Day's left as the entertaining end to the first half continued.
Salford's pressure eventually told in stoppage time though when Hendry netted from inside the six-yard box, with that save unstoppable, even for an in-form Day.
Unfortunately, the second half continued from where the first left off, as Salford completed the turnaround with McAleny finding the bottom right corner after a fine solo run into the County box.
Charsley tried to answer straight back for Newport, but his strike from range was well caught by Cairns.
Ryan Leak flicked over the bar after a corner from the right though as Salford didn't let up in their attempt to extend their lead.
We kept going too though, as Aaron Lewis had a go from the edge of the box, but shot narrowly wide of the right post.
Charsley later struck a half-volley wide after Cam Norman's cross was chested to Charsley by Lewis, with the ball coming off the wrong part of Charsley's boot and going past the near post.
Luke Bolton then curled over for Salford before the towering Matt Smith headed a crossed free-kick from the left by Elliot Watt wide of the post from inside the six-yard box.
Our final chance saw Farquharson header over a cross from the right before Salford sealed the contest through Matt Smith in second half stoppage time.
Watt's corner from the left was headed home by Smith, with Bogle on the line unable to keep it out.
Salford City: Alex Cairns, Ibou Touray (C) Jason Lowe, Elliot Watt, Matt Lund (Stephen Mallan '64), Callum Hendry, Ethan Galbraith (Matt Smith '68), Louie Barry, Luke Bolton, Richard Nartey (Conor McAleny '39, Theo Vassell '73), Ryan Leak
Subs not used: Giosue Bellagambi, Callum Morton, Shane McLoughlin
Newport County: Joe Day, James Clarke (James Waite '87), Priestley Farquharson, Mickey Demetriou (C), Cameron Norman, Aaron Lewis, Matt Baker (Aaron Wildig '68), Nathan Moriah-Welsh (Kiban Rai ''87), Harry Charsley (Will Evans '78), Omar Bogle, Charlie McNeill (Calum Kavanagh '64)
Subs not used: Nick Townsend, Scot Bennett