The Crows kicked six goals to two in the last quarter for a gutsy 15.11 (101) to 13.9 (87) triumph in a Friday night thriller.
Adelaide slipped 32 points down late in the first term before a sell-out 50,654-strong crowd at Adelaide Oval.
They recovered to take the lead, only to lose it and trail by eight points at three-quarter time.
The Crows, with stars Izak Rankine and Taylor Walker kicking two goals each in a final term, then finished with a flourish.
Walker converted two long-range set shots to seal victory - he kicked three goals for the game, as did Rankine, while spearhead Riley Thilthorpe booted four.
"There was a lot of pressure coming in - massive, massive stage," Nicks said.
"And then to start the way we did, the pressure went through the roof.
"To reset the way we did, the maturity our boys showed ... it was another way to win in what was a finals atmosphere."
Adelaide sit top with a 15-5 win-loss record but Collingwood will reclaim pole position with a victory over Brisbane on Saturday night.
Hawthorn (13-7) remain fifth - only a win ahead of ninth spot - with fresh concern over injury-troubled midfielder Will Day, who limped from the field late on.
"I don't have an answer yet," Hawks coach Sam Mitchell said of Day's condition.
"He was cramping, he had ice on most parts of his lower body, as plenty of the players do, so unsure just yet."
The Crows were superbly served by Irish-born defender Mark Keane (21 disposals, six marks), halfback Wayne Milera (19 touches) and winger Dan Curtin (20, six inside 50s).
Attacking trio Thilthorpe, Rankine and Walker were ever-present threats while captain Jordan Dawson (21 disposals, 11 tackles) kicked two team-lifting goals in five minutes.
Hawthorn stalwart Jack Gunston booted four goals and Jack Ginnivan (19 disposals) scored two.
Hawk duo Massimo D'Ambrosio (25 possessions) and Karl Amon (23) were standouts and skipper James Sicily ruled the air with 11 marks.
In a wildly fluctuating fixture, Hawthorn raced to a 32-point lead - 5.3 to 0.1 - late in the first quarter.
The Crows hit back with 6.6 to nothing in the second term for a 16-point halftime advantage.
Adelaide went 18 points clear before a steely response from the Hawks: six of the next seven goals for an eight-point edge at the final change.
The Crows logged three consecutive goals to jump 12 points up before two strikes from Gunston, both from holding free kicks, put the Hawks one point ahead.
Adelaide rallied with the final three goals of the game, with Walker's last two long bombs sending the sell-out crowd into raptures.
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