The Bees had the better of the opening 20 minutes against their higher placed hosts, controlling possession , though the first chance of note fell Fylde’s way on 24 minutes, when Bees keeper Mark Cousins pushed Haughton’s ferocious volley wide for a corner.
Three minutes later, Cousins’ opposite number Jay Lynch was called into action at the other end, clearing a curling effort by Medy Elito which looked destined to nestle in the top corner.
Both sides had one more opportunity just before the interval, Wes Fonguck fired straight at Lynch, while substitute Alex Reid’s header was off target.
Barnet would have the first opportunity of the second half when Shaq Coulthirst curled a shot just wide of the right post four minutes in.
A good run by Haughton set up a further shooting chance 10 minutes later but his effort was blocked.
Fylde pressed in the dying minutes in a bid to avoid extra-time but two Haughton efforts flew wide as did one in between by Zaine Francis-Angol.
Fylde took carried this momentum into the opening exchanges of extra-time, Cousins forced into saves from Philliskirk and Haughton.
But four minutes before the break, Barnet had the best chance so far when Fonguck’s great low cross found substutite Simeon Akinola at the far post but somehow his effort was blocked on the line.
There were worried moments for Fylde five minutes into the second period as Lynch saved from Akinola and fellow sub Barham shot wide from close range on the follow up.
An unmarked Akinola had one more chance but headed over from six yards out and when Haughton’s final effort at the other end was stopped by Cousins the tie went to penalties.
Fylde made no mistake with their first when Philliskirk fired into the roof of the net.
Captain Callum Reynolds then stepped up for Barnet but his spot kick cannoned back of the crossbar.
Haughton then gave Fylde a two goal advantage before Barham buried his spot kick into the bottom corner.
Bond made it 3-1 before Fonguck hit the post, making it match point Fylde.
Alex Reid stepped up and fired his spot kick home, winning the shootout 4-1.
BARNET – Cousins, Johnson, Reynolds, Robson, Coulthirst, Taylor, Boucaud (Charles 105), Fonguck, Elito (Barham 64), Sweeney, Mason-Clark (Akinola 96)
Unused subs: Matrevics, Alexander