The Crows were chasing their first win at GMHBA Stadium since June 2003 on Thursday and seeking a response to last week's loss to the Western Bulldogs.
Geelong dominated early and led until Alex Neal-Bullen put Adelaide in front five minutes into the fourth quarter.
But the Cats regained control to snag a 9.14 (68) to 9.6 (60) win, condemning Adelaide to a 1-2 start and improving their own record to 2-1 ahead of the Easter Monday clash with Hawthorn.
Geelong had the first 10 inside-50s in wet conditions and led by 14 at quarter-time - and for Nicks, the slow start was the difference.
"Probably the first 10 minutes of the game we were still on the bus," Nicks said.
"But again we showed we can fight back from it. Unfortunately, when you're doing that against the best teams you're going to walk in after a game and be disappointed in a close loss. We'd like to be better than that.
"It's a tough one to swallow when you start like that and you fight back to get in front, especially at a hostile ground like this."
Adelaide were without skipper Jordan Dawson (calf), veteran forward Taylor Walker (managed), recruit Callum Ah Chee (hamstring) and Rory Laird (calf), while Geelong missed skipper Patrick Dangerfield (calf).
Geelong dominated but were nearly left to rue poor connection in attack.
"Potentially, it was going to be a really frustrating night for us because even though we weren't executing very well, it felt like we had control of the game for large periods," Cats coach Chris Scott said.
"But in the end, it was probably a game where the weight of numbers was enough, but it certainly wasn't the spectacle that it could have been."
Cats Bailey Smith (39 disposals), Max Holmes (27 disposals), Tom Stewart and Sam De Koning were prolific.
Jack Martin (three goals) and Ollie Dempsey (two goals) did the damage in attack while Oisin Mullin limited Izak Rankine.
Adelaide's Josh Rachele (31 disposals, seven clearances), Sam Berry (nine clearances), Josh Worrell (30 disposals) and Zac Taylor (three goals) stepped up.
Jeremy Cameron and Shannon Neale were held goalless by Max Michalanney and Nick Murray respectively.
In the second term, Adelaide nabbed three consecutive goals - with Rankine kicking one and creating another - and trailed by six at halftime, then four at the final change.
Early in the final term, Crows star Riley Thilthorpe outpointed O'Sullivan then teed up Neal-Bullen to put Adelaide in front.
But Geelong peppered the goals before Martin shimmied away and kicked his third to restore an eight-point buffer.
The goal came just after a last disposal free kick had gone Geelong's way when it should have been Adelaide's, but Nicks wouldn't buy into the impact that had on the game.
Adelaide will lick their wounds before hosting Fremantle next Friday.
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