Honours were deservedly equal in this top-of-the-table contest at Derby's Mickleover base.
The first chance of note fell to the hosts' Precious Hamilton, who volleyed wide after 23 minutes.
Just past the half-hour, Fylde keeper Ellie Etheridge was called into action but got down well to save.
More saves followed by the alert keeper in the minutes approaching half-time, while a good block by Alex Taylor also denied Derby, for whom Ellie Gilliatt shot over.
Fylde's best chance of the half came in stoppage time, when Jodie Redgrave got on the end of a Lauren Merrin cross.
Derby keeper Sarah Morgan parried the shot but Fylde couldn't finish in the scramble which followed.
Etheridge continued to keep Derby at bay after the restart, while Morgan was also tested at the other end but saved a Faye McCoy header well in the 64th minute.
McCoy went close again with a curling shot seven minutes later, while Hannah Forster's effort from long-range narrowly missed the target.
The best of the last chances went to McCoy, who shot wide from distance before seeing a header from Hannah Fryer's cross saved.
This point in the competition's only match played on Sunday saw Fylde climb above Wolverhampton Wanderers into second place, three points behind Derby going into the Christmas break.
Fylde; Etheridge, Taylor, Forster, Fuller, Holbrook, Hollingshead (Donoghue 77), Merrin, Fryer, Hughes (Rowe 70), McCoy; subs: Young, Bartley, Whitaker.
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