Dom Telford's 13th goal of the season rescued a point in Sussex as County played out a 1-1 draw with Crawley Town
Appiah headed Crawley into a 55th-minute lead after meeting Jack Powell's whipped in free-kick from the right.
But Telford struck back in the 83rd minute to ensure both sides went home with a share of the spoils.
A quiet first half saw its first half-chance when County defender Mickey Demetriou hit a side-foot volley straight at Crawley keeper Glenn Morris, who saved comfortably.
The first major opening of the opening 45 came after 25 minutes but Finn Azaz knocked his effort from close range just past the right-hand post.
Kevin Ellison, starting ahead of Courtney Baker-Richardson, gave Morris his first real problem of the match and the Crawley stopper did well to tip a fierce drive from the 42-year-old forward wide of the post with the corner leading to Cameron Norman having a shot that went out for a throw-in.
The only other talking point of the first half was Aaron Lewis being brought down in the box just before the break but the referee waved play on.
County captain Matt Dolan had to go off injured in the 53rd minute and a bad start to the second half got worse for Newport when, two minutes later, Appiah headed Crawley into the lead.
Joe Day then needed to get down well to deny Crawley skipper George Francomb to deny him from close range before half-time substitute Will Ferry hit an effort across goal for the Red Devils from the left of the box.
Soon after, Ferry shot over the bar from a tight angle as the hosts pushed for the second goal. Ferry had to be sub-subbed though after pulling up with injury after taking the shot.
County were kept at bay by the Crawley defence, with Azaz being limited to a wayward shot wide from distance in an attempt to level proceedings.
That was until, with seven minutes to go, who else but Telford to slot home from about 12 yards out to keep up his incredible scoring streak.
It was Crawley who came closest to grabbing all three points though as Appiah hit the bar with a flicked effort over Day with a minute to go and, in stoppage time, Day made a superb diving save to his right to deny Reece Grego-Cox.
Crawley Town: Glenn Morris, George Francomb (C), Ludwig Francillitte, Tony Craig, Archie Davies, James Tilley (Reece Grego-Cox '67), Jake Hessenthaler, Jack Powell, Tyler Frost (Will Ferry '45 ((Tom Nichols '72)), Ashley Nadesan, Kwesi Appiah
Subs not used: Blondy Nna Noukeu, Szymon Kowalczyk, Amrit Bansal-McNulty, Alex Battle
Newport County: Joe Day, Cameron Norman, Ed Upson (Alex Fisher '83), James Clarke, Matt Dolan (C) (Jake Cain '53), Aaron Lewis, Finn Azaz, Dom Telford, Kevin Ellison (Courtney Baker-Richardson '57), Mickey Demetriou, Oliver Cooper
Subs not used: Nick Townsend, Ryan Haynes, Timmy Abraham, Scot Bennett