The Clarets were three goals up at half-time but had to withstand a brave fightback by Kim Turner’s side in this second-round tie between the Lancashire rivals from the National League Northern Premier Division.
Fylde had the first effort of note at Kellamergh Park in the 12th minute, when Emily Hollingshead’s shot was turned away for a corner.
Jodie Redgrave shot over the top before Burnley opened the scoring after 20 minutes with a long-range Millie Ravening strike.
Burnley keeper Lauren Bracewell denied Hollingshead and Hannah Forster on the day she became the first player to make 100 Fylde appearances.
The Clarets’ Evie Priestley headed against the bar before setting up teammate Katie Thomas for their second on 29 minutes.
It got worse for the hosts when Lizzie Hamer lobbed their third two minutes later.
Sasha Rowe shot over the bar as the first half ended with Fylde three goals down.
They had it all to do in the second half but set about their task with gusto as Hollingshead’s cross flew just wide.
And they gained a lifelife on the hour, when Holbrook shot home on the half-volley.
Fylde had a let-off when Burnley struck a post but the comeback continued in the 74th minute.
Alex Taylor’s low drive went out for a corner and Holbrook’s delivery reached substitute Amy Hughes, who made it 3-2.
Fylde had chances for an equaliser but substitute Mel Bartley’s effort from a Hughes corner was cleared.
Fylde have defeated Burnley in the league this season but the Clarets continue to have the edge on them in the FA Cup.
Fylde: Smith, Taylor, Forster, Fuller, Holbrook (Bartley 82), Hollingshead, Merrin, Redgrave (Donoghue 66), Rowe (Hughes 65), Fryer, McCoy
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