Gould was an early casualty, but the setback didn't prevent the Crows grinding out a tough 7.6 (48) to 4.3 (27) win at Frankston's Kinetic Stadium on Sunday.
Anne Hatchard (29 disposals, two goals), Ebony Marinoff (32 touches), Sarah Goodwin (25) and Madison Newman (28) all shone for Matthew Clarke's side.
Eloise Jones kicked two goals from 14 disposals and the result gave Adelaide a 3-2 record, while Hawthorn slip to 4-1 after five rounds.
The Crows' ability to control play kicking against a stiff breeze in the second and fourth quarters was a feature of their victory.
"Each game is like a final with a short season ... so it was nice to be able to get the win," Adelaide veteran Chelsea Randall told Fox Footy.
"It was pretty windy once we got out in the middle of the ground but both teams showed a bit more composure when they were actually going into the wind.
"Sometimes when you get excited with the wind you just blast away.
"That can happen, but we managed to control the ball up the other end, which was good."
Gould fell heavily in a marking contest early in the match and was taken to hospital for scans on her left wrist.
"It didn't look great ... fingers crossed, but not looking awesome," Crows coach Clarke told Fox Footy.
Adelaide managed the only two scores of a scrappy first term with the wind at their backs, leading 0.2 to 0.0 at quarter-time.
The visitors' advantage didn't last long after the first change as Elli Symonds broke the goal drought and put the Hawks in front with her first AFLW major.
But Adelaide steadied, with goals from Jones and Hatchard giving them an eight-point buffer at the main break.
It grew to 16 points by the final change, as further goals to Danielle Ponter and Jones extended the advantage in the Crows' dominant third term.
Adelaide put the result to bed when Hatchard and Teah Charlton kicked the first two goals of the last quarter.
Charlton's sealer was a nice moment for the Crows midfielder, a week after she gave away a downfield free kick that gifted Brisbane victory in the dying stages of their round-four clash.
Tilly Lucas-Rodd (24 touches) and Eliza West (22) fought hard for Hawthorn, as did ruck Lucy Wales, who finished with 26 hit-outs, 19 disposals and six clearances.
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