The Crows trailed for much of Saturday's Adelaide Oval thriller before steaming to a 11.13 (79) to 9.8 (62) triumph with a final-quarter flourish.
Adelaide took fifth spot from Melbourne with their fourth win by three goals or less this season - they logged 10 scoring shots to one in a frenetic final term, including two goals in the last seven minutes.
Crows boss Nicks was rapt at the rugged nature of victory in a game both coaches rated as finals-like.
"We won that one in a different way," Nicks said.
"What this one did was just add more momentum and belief to where we're at post the bye."
Since their bye, Adelaide have pipped Geelong by one point in a wet nerve-jangler, blown away the Western Bulldogs by 57 under the Marvel Stadium roof, and trumped the Demons in a bruising battle.
"We've had three really tough opponents that are all fighting for the same thing we're fighting for," Nicks said.
"It's even more pleasing when you're able to do it against a team that's in good form, because you take a lot of belief.
"Especially towards the end of that game, that last quarter, to finish it off the way we did ... they were so organised, the guys were disciplined."
Adelaide's win came amid concern over club icon Tony Modra, who was seriously injured in a truck accident on Thursday evening.
Modra woke on Saturday, a day after having facial surgery, and remains in hospital in a stable condition.
"There's a lot of positive news coming back, but we don't want to get ahead of ourselves," Nicks said.
"It's a tough time because he's such a huge presence around our footy club."
The Crows (nine wins, five losses) claimed fifth spot from the Demons (nine wins, six losses), who now have their bye.
Melbourne led at the quarter breaks by eight, one and two points before being steamrolled.
"It came down to execution - fundamentals under pressure," Demons coach Steven King said.
"Certainly frustrating, but I can't fault out our group's endeavour.
"That was a finals-type pressure and atmosphere, so that's a bonus for us. That will be a great experience to take with us and improve on."
The game's brightest stars - Adelaide captain Jordan Dawson (18 disposals, two goals) and Melbourne's Kysaiah Pickett - were, by their lofty standards, subdued.
Pickett was restricted to 15 touches by Crow James Peatling and shifted forward, with no impact, in the final term.
Peatling also gathered 15 disposals, while his teammate Josh Rachele slotted three goals, including two clutch majors in the final quarter.
Adelaide defenders Wayne Milera (27 disposals, one goal) and Rory Laird (26 possessions) were outstanding, and Sam Berry's stellar season continued with 24 possessions, seven clearances and eight score involvements.
Melbourne captain Max Gawn was superb with 28 disposals, 31 hitouts and six inside-50s, and Jacob van Rooyen kicked three goals - all in the first term.
Tom Sparrow (28 disposals, seven clearances, seven inside-50s) was a force, Jake Lever, in his 200th AFL game and against his former club, was influential in defence, and Jake Bowey (24 touches) and Daniel Turner (22) were other key ball-winners.
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