Crook excelled to keep out Haughton's driven spot-kick, but the Fylde playmaker squeezed home the loose ball to seal victory for the title favourites nine minutes from time.
Fylde were indebted to their own keeper Chris Neal for a hat-trick of fabulous second half saves to deny Paul Green, Danny Elliott and substitute Jordan Burrow.
The full-time Coasters dictated much of the first half play, but found United a well-drilled and resilient opponent. Midfielder Danny Philliskirk headed wide from Fylde's best early opportunity.
Tom Platt also headed wide when well-placed from a Terry Hawkridge corner, while Elliott crashed an effort off target after some silky footwork.
The Pilgrims lost the services of full-back Matt Tootle four minutes before half-time, with midfielder Green slotting in at right-back and Keenan Ferguson moving across to the left.
Neal made fine stops on 70 and 74 minutes respectively to keep Green and Elliott at bay but Fylde struck the decisive blow when Scott Garner was penalised for tripping HAUGHTON and the Fylde talisman fired home the rebound from a brilliant initial save from Crook.
Neal subsequently got himself behind a firm Jordan Preston drive, before saving his best until last by clawing away Burrow's goalbound header in stoppage time.
AFC Fylde (4-2-3-1): Chris Neal; Luke Burke, Alex Whitmore, Jamie Stott, Luke Conlan; Danny Philliskirk, Luke Joyce (Liam Nolan 86); Ben Tollitt, Nick Haughton (Jacob Holland-Wilkinson 90), Sam Osborne (Stephen Dobbie 61); Joe Piggott. Subs (not used): David Perkins, Bobby Jones (gk).
Boston (4-3-3): Peter Crook; Keenan Ferguson, Luke Shiels, Scott Garner, Matt Tootle (Paul Green 41); Shane Byrne (Jordan Burrow 83), Tom Platt, Connor Dimaio; Terry Hawkridge (Jake Wright Snr 59), Danny Elliott, Jordan Preston. Subs (not used): Andi Thanoj, Fraser Preston.
Referee: Sam Mulhall.
Attendance: 1,166.
PIC: Eric Brown.