The Dockers scored 6.7 (43) over four quarters of football but were matched by the more accurate Giants 7.1 (43) as the two teams played out the first ever AFLW draw.
A hard-working Lara Filocamo gathered a team-high 19 disposals for Fremantle while Ashley Sharp kicked two goals.
For the Giants, Phoebe McWill-iams kicked two goals and Emma Swanson racked up 16 disposals.
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READ NOWFremantle next host Adelaide at Fremantle Oval on Sunday, still chasing its first win of the new competition.