The Crows trailed by 25 points at quarter-time but prevailed 9.5 (59) to 8.8 (56) at Adelaide Oval on Saturday night - their first win against the Pies since 2016.
Adelaide (68 premiership points) will finish first entering the finals if they defeat 17th-placed North Melbourne next Saturday.
Collingwood (60 points), with five losses from their past six games, are fourth and in a logjam jostling for positions ahead of their Friday-night fixture against Melbourne.
The Crows had lost their past 10 games against Collingwood, preceded by a 2017 draw.
But with victory before a sold-out crowd of 54,283 - the second-largest attendance at an AFL game at the Oval - Adelaide equalled their club-best returns of 17 wins and five losses in 2005 and 2012 - a win over the Roos will create a new benchmark.
"We didn't play our best footy and we found a way (to win)," Adelaide coach Matthew Nicks said.
"I know the belief is there, we know how to win."
The Crows were jumped by a fast-starting Collingwood, who produced a first-term blitz to create a 25-point quarter-time lead, 5.3 to 1.2.
But Adelaide flipped the script in the second term, with ex-captain Taylor Walker kicking two of five unanswered goals for the hosts.
A late strike from Izak Rankine gave Adelaide a five-point edge at halftime, 6.3 to 5.4.
The third quarter, amid rain, was tight - neither team managed a goal until Adelaide's Isaac Cumming scored in the 27th minute.
But Pie forward Jamie Elliott replied, threading a set shot from an acute angle, to reduce Adelaide's advantage to two points at three-quarter time, 7.6 to 6.8.
Another scoring stalemate ensued in a tense finale: a goalless 17-minute stretch was broken when Crow James Peatling snapped accurately.
But Magpie Jack Crisp responded six minutes later to reduce the margin to three points, only for key Crow Riley Thilthorpe to then take a superb contested mark and convert.
Again the Pies responded, with a long bomb from Nick Daicos leaving the visitors three points down with almost four minutes remaining, but Adelaide grimly held on for victory.
"We didn't quite get the four points but we leave here not with our tail between our legs," Collingwood coach Craig McRae said.
"It was a hard game, a finals-type game ... it was a real tactical battle."
Ex-Crow skipper Walker and Darcy Fogarty kicked two goals each, while defenders Josh Worrell (27 disposals), Mark Keane (23) - who rebounded the ball from Adelaide's defensive 50m arc some 13 times - and captain Jordan Dawson (23) were influential.
Collingwood's Nick Daicos was superb with a game-high 29 possessions and a goal.
Veteran Scott Pendlebury (24 touches) was prominent, especially early, Darcy Cameron (23 disposals) ruled the rucks, and forwards Elliott and Tim Membrey booted two majors apiece.
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