The Crows mounted a late challenge and took the lead early in the final quarter, but goals to Michael Barlow and late inclusion Cameron Sutcliffe ensured the Dockers edged home, the visitors winning 10.6 (66) to 8.11 (59).
Five talking points: Crows v Dockers
Barlow was in superb touch for Fremantle with 32 disposals, eight tackles and a goal while defender Michael Johnson (19 touches, nine marks) was sensational in defence.
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Dockers coach Ross Lyon said that while he was pleased with the interstate win, his side still had a long way to go before it could start thinking finals.
"The bottom line is we're two and a half wins ahead of 12th, which is the Gold Coast, with over half the season to go," Lyon said.
"We've got nothing to be pleased about bar the fact that we're in a position where we can control our own destiny, but we're far from where we want to be.
"You've got to earn the right to play finals and until you earn that right it's about home and away focus."
As if on cue, the first official day of winter arrived with soaking conditions and it spurred Adelaide to replace key forward Shaun McKernan with a smaller, more weather-appropriate option in Brodie Martin.
The conditions suited Crows workhorse Rory Sloane to a tee and early signs suggested a prolific performance from the 23-year-old.
He had 10 first-term disposals and finished with 30.
Patrick Dangerfield was at his best as well with 21 possessions and three goals, while ruckman Sam Jacobs ended his run of poor form with 50 hit-outs.
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Last week's hero Jared Petrenko kicked Adelaide's third goal, but the Crows were forced to rue missed opportunities when Docker Nick Suban's second goal handed the visitors the lead 10 minutes into the second quarter.
They extended it to 11 points through Nat Fyfe, and while Crows Brodie Smith and Andy Otten were impressive across half-back, their teammates struggled to work the ball past half-forward.
When Adelaide did manage to attack, Johnson and Paul Duffield were there waiting.
Crows coach Brenton Sanderson said his side struggled to deal with Fremantle's extreme pressure.
"We were handballing it backwards when we should’ve been surging it forwards," Sanderson said.
"Their pressure at times, we couldn’t handle [it].
"We just gifted them momentum when we shouldn’t have."
The third term loomed vital for the Crows and after Fremantle appeared be in control of the contest, a long-range goal from Jason Porplyzia re-ignited Adelaide's hopes.
A quick goal or two might have been enough for the Dockers to ice the game in the last, but it was Adelaide who goaled first through Richard Douglas, reducing the margin to just four points.
Dangerfield thought he had given his side the lead at the 13-minute mark, but after nearly a minute of consultation the umpires decided to review his shot at goal, which was eventually deemed to have nicked the post.
There was no such confusion over his second shot, 'Danger' snapping truly within 30 seconds of his miss.
The lead was short-lived though, with Barlow then Sutcliffe sealing the game.