The 17.9 (111) to 12.12 (84) win came on the back of a big second quarter, in which the Magpies booted seven goals to two to turn a 25-point quarter-time deficit into a four-point half-time lead.
The Crows continued to fight hard and were within eight points as late as 18 minutes into a gripping final quarter, but could never re-claim the lead.
The result means Adelaide has lost all six of its games against top eight teams this season, and as good as ends the 2012 preliminary finalists' slim hopes of playing off in September.
In a further blow for the visitors, star midfielder Patrick Dangerfield appears set to spend time on the sidelines after injuring his right shoulder.
Collingwood now has 10 wins for the season, moving it to sixth on the ladder, although it will fall back to seventh if Richmond defeats Gold Coast on Saturday.
Much like in last week's 41-point thrashing of Carlton, the move of Ben Reid from defence to the forward line proved pivotal in turning around the Magpies' fortunes.
The key position swingman booted the first two goals after quarter-time as the home team awoke from its sluggish start.
Small forward Andrew Krakouer then injected himself into the action, booting all of his three goals in the 15 minutes before the main break.
Collingwood midfield stars Dane Swan (31 disposals) and Scott Pendlebury (a career-best 42 touches) shared best afield honours, with both booting crucial goals in the final quarter as Adelaide pressed.
It was the 36th time the duo has both had 30 possessions in the same game, and the Magpies have won 32 of those games.
In his first game of the season after battling a quad injury all year, 2012 Copeland Trophy winner Dayne Beams was also busy, gathering 25 possessions.
His clean ball handling and crisp ball use was a welcome addition to Collingwood's midfield.
Luke Ball, in his 200th match, and Steele Sidebottom, in his 100th, were other strong contributors, as was youngster Marley Williams in defence.
Adelaide had only four goalkickers, with Tom Lynch and Jarryd Lyons booting four, Jason Porplyzia three and Richard Douglas one.
Lyons had only one career goal to his name before Friday night's clash.
First-year player Brad Crouch was a standout for the Crows in the midfield, using the ball with precision by foot.
Ricky Henderson also gave his all, while Ben Rutten was typically solid down back.
Dangerfield injured his shoulder in the first quarter when he collided with opponent Sam Dwyer as the pair attacked a ground ball.
After having the shoulder strapped, Dangerfield bravely returned to the ground, but he was heavily restricted in movement and unable to exert his usual influence on the game.
The Crows are now 6-9, and could finish the weekend as far as three games plus percentage out of the top eight if Port Adelaide beats Hawthorn on Saturday.
They return home to Adelaide to face Geelong next week, while Collingwood will aim for a sixth win in seven matches when it takes on Gold Coast at Metricon Stadium.
The crowd set a record for a home and away clash between the two teams.
Collingwood 2.2 (14) 9.5 (59) 13.6 (84) 17.9 (111)
Adelaide 6.3 (39) 8.7 (55) 10.11 (71) 12.12 (84)
Goals - Collingwood: Krakouer 3, Pendelbury 2, Swan 2, Reid 2, Macaffer 2, Cloke 2, Witts, Ball, Sidebottom, Williams
Adelaide: Lyons 4, Lynch 4, Porplyzia 3, Douglas
Best - Collingwood: Pendlebury, Swan, Ball, Beams, Dwyer, Cloke
Adelaide: Lynch, Lyons, Crouch, Henderson, Douglas, Porplyzia
Injuries - ?Collingwood: TBC
Adelaide: Dangerfield (right shoulder)
Substitutes - Collingwood: Josh Thomas replaced Jamie Elliott in the fourth quarter
?Adelaide: Matthew Jaensch replaced Matthew Wright at three-quarter time
Reports: Nil
Umpires: McBurney, Stevic, Stewart
Official crowd: 54,790 at the MCG
