The 21-year-old former Leeds striker headed the League Two side in front after 32 minutes and doubled the advantage before the break when he turned in Padraig Amond's cross.
Hatfield then completed his hat-trick and added a fourth nine minutes later to ensure Leam Richardson enjoyed the perfect start to life as Accrington manager, despite Adam Farrell's late consolation.
Hatfield wasted two early chances and Fylde, managed by former Tranmere defender Dave Challinor, threatened themselves when Michael Barnes' shot was blocked.
Lee Molyneux then hit a post before his cross from the left was headed in by Hatfield, with the Accrington man doubling his haul on the stroke of half-time.
Hatfield secured the match ball in the 77th minute, firing in from 10 yards after Amond's cross had led to a goalmouth scramble. The Accrington striker rubbed salt in the wound by adding a fourth after 86 minutes and though Farrell turned in Richie Allen's late cross, it was far too little, too late to save Fylde's cup dream.