The Crows broke clear in the final quarter to defeat the Power by 31 points in an epic Showdown at Adelaide Oval.
In Saturday's other results, St Kilda continued its dream start under coach Ross Lyon with an 18-point triumph over Essendon, while Carlton defeated GWS by 10 points and Hawthorn claimed its first win over the season with a 19-point victory over North Melbourne.
In Adelaide, Crows captain Jordan Dawson won the Showdown Medal as star recruit Izaak Rankine, young key forward Riley Thilthorpe and stalwarts Rory Sloane and Rory Laird shone in the 18.9 (117) to 13.8 (86) win.
It is Adelaide's first victory of the season and leaves the fierce local rivals with 1-2 records.
Rankine kicked a goal after the final siren to cap his star performance, with the former Gold Coast forward kicking four majors.
With Darcy Fogarty injured, Thilthorpe stood up and kicked a career-best five goals.
The Power had won five of the past six Showdowns and also had a major victory ahead of this match, striking a deal with Collingwood that allowed them to wear their traditional black-and-white "prison bar" guernsey.
They started favourites in their home match, but the Crows ran over the top of them after a pulsating duel, with seven goals to two in the last term.
Adelaide sprung a tactical surprise, playing Dawson in the midfield rather than his usual defensive role, and he was massive early.
Dawson was mighty with 12 contested possessions, but Rankine, Laird and Thilthorpe had even bigger games in a famous Crows win.
The Power kicked the first two goals, but Adelaide hit back immediately in a frantic start that set the stage for a titanic struggle.
There was controversy when Adelaide defender Lachie Sholl took a mark, went slightly off his line and was tackled by Sam Powell-Pepper, who kicked the goal when it should have been a Crows clearance out of danger.
After taking a one-goal lead into quarter-time, the Power broke out to a 17-point advantage in the second term and looked like they might be about to take control.
But the Crows kicked the last three goals of the half and fittingly scores were level at the main break.
The intensity of the match was summed up at the start of the third term when Crows teenager Max Michalanney was ironed out by Rowan Marshall.
Michalanney, Adelaide's first father-son recruit, was charging at full pace after the ball when Marshall came from the other direction and cleaned him up with a brutal front-on bump.
It was a fair hit that sent Michalanney to the bench with sore ribs, but the 19-year-old sucked it up and returned to the field to be among the Crows' best.
With the pressure enormous, the two teams went goal-for-goal before Adelaide blew some chances late in the third term and led by three points at the last change.
The Power kicked two of the first three goals in the last quarter and led by four points at 10 minutes.
Junior Rioli dropped a mark in attack and Rankine then won a critical ball on the wing, setting up Lachie Murphy for a goal that gave Adelaide back the lead.
That opened the floodgates, with the Crows kicking the last six goals of the match.
Conor Rozee starred for the Power as Powell-Pepper and Charlie Dixon kicked three goals apiece.
Saints continue revival under Lyon
St Kilda celebrated its 150th anniversary in style with a gritty three-goal win over Essendon at the MCG.
Jack Higgins and Dan Butler kicked four goals each for the Saints, whose blistering opening and stifling defence were features of the 14.8 (92) to 11.8 (74) victory.
But there were some nervous moments in the final term when the Bombers drew level — having trailed by 34 points early in the match — before St Kilda steadied with a five-goal burst to put the result to bed.
It improved the Saints' record to 3-0 under Lyon this season, while Brad Scott was dealt his first loss in charge of Essendon.
Tony Lockett, Ian Stewart, Ross Smith, Barry Breen and Nicky Winmar were among the St Kilda greats on hand to help celebrate the club's milestone in front of a 69,251-strong crowd.
The faithful who turned up got their money's worth as witnesses to a rollercoaster ride of a contest.
The Saints' opening two goals were gifts from 50-metre penalties against Mason Redman and they had the first five majors on the board before time-on in the first term.
Late to the party, Essendon trailed by 27 points at quarter-time.
Momentum swung around the contest when the Bombers lifted their intensity, with Will Setterfield setting an example.
Essendon moved Kyle Langford forward at the final change and kicked the first three goals of the final term.
A pair of Jye Caldwell snaps came either side of Langford's toe-poke on the line.
But Higgins and Jade Gresham provided quick replies for the Saints, who booted five successive goals as they kicked into party mode.
Brad Crouch (31 disposals), Jack Sinclair (26), Mason Wood (27), Seb Ross (24) and Gresham (23) were all strong contributors.
Nic Martin (27 disposals) was among the Bombers' best and Darcy Parish racked up 34 touches, with Caldwell and Archie Perkins kicking two goals each.
Jordan Ridley and Jake Kelly were solid in defence but explosive forward Jake Stringer had little impact on return from injury, kicking one goal from eight disposals.
As part of their 150th celebrations, St Kilda inducted former star players Leigh Montanga and Nick Dal Santo into the club's Hall of Fame.
Champion full-forward Bill Mohr was posthumously elevated to Legend status at the Saints.
Blues prevail against Giants
Carlton overcame a spirited GWS challenge with a controversial decision in its favour and a late goal to Charlie Curnow sealing their triumph at Giants Stadium.
While Curnow kicked the last major of the match with fewer than three minutes remaining, it was captain Patrick Cripps who inspired the Blues to their 9.20 (74) to 9.10 (64) victory.
The Blues were almost made to pay for their profligacy in front of goal, especially after they only managed five behinds from 15 inside-50s in the third term to leave the door open for the Giants.
GWS kicked three consecutive goals either side of the last change to claim the lead until the Blues were awarded a controversial free kick in the goal square when Stephen Coniglio disputed a decision.
Jesse Motlop made the most of the umpire's call to put the Blues back in front at the 15-minute mark as the teams battled it out between the arcs until Curnow's final intervention.
Cripps and Giants young gun Tom Green went head-to-head for much of the contest in an enthralling duel between the on-ball master and apprentice.
Cripps was superb for the Blues with match-highs for disposals (42), clearances (13) and score involvements (11), while Green amassed 34 touches and seven clearances.
The Blues' (2-1) runners and clean ball-users Sam Docherty (39 disposals, one goal), Adam Cerra (28 disposals) and Adam Saad (23) were also influential, but Nic Newman arguably had even more of an impact on the result.
The halfback clamped down on Toby Greene to restrict the Giants captain to only five disposals and one goal while gathering 24 touches himself.
Matthew Owies slotted two of the Blues' early majors but was subbed out in the second term due to a hamstring injury, while Curnow also finished with two.
The Giants were boosted by the return of Josh Kelly (30 disposals, one goal) and Lachie Whitfield (27) from concussion, while Coniglio (29) will be disappointed by the late call against him but continued his superb start to the season.
On a tough day for tall forwards in blustery conditions, the Giants' Jake Riccardi kicked his first two goals of the season, while Jesse Hogan also booted two.
Hawks notch first win
Sam Mitchell has struck the first blow in his coaching rivalry with former mentor Alastair Clarkson, with Hawthorn holding off a final-quarter surge from North Melbourne.
The Hawks looked in total control in the first half but a run of five consecutive North Melbourne goals trimmed the margin to just three points midway through the final quarter before Hawthorn steadied, running out winners 11.14 (80) to 9.7 (61) in Launceston.
It was the Hawks' opening victory of the season, and a first defeat for the Kangaroos.
The Kangaroos laid just 16 tackles and had 56 fewer uncontested possessions in a lacklustre first half and while they raised their intensity to challenge thereafter, the damage was done.
With co-captain Jy Simpkin missing through suspension, North Melbourne's midfield was dealt another huge blow minutes before the opening bounce, when gun midfielder Luke Davies-Uniacke withdrew with calf tightness.
Hawthorn's young midfield were able to hold their own around stoppages, allowing defenders such as James Sicily (28 disposals, 18 marks), Jack Scrimshaw (25 disposals, nine marks) and Blake Hardwick (23 disposals, 11 marks) to control the match from half back.
The Hawks' ability to pick through North Melbourne's defensive zone with patient, precise ball movement and a willingness to take risks by foot allowed them to finish with 80 more uncontested possessions and 51 more marks.
Dylan Moore showed his class and creativity throughout, setting up a string of goals, while Will Day worked tirelessly in the middle, notching 28 possessions.
Lively small forward Tyler Brockman kicked three goals in his first match since 2021, while Fergus Greene proved a dangerous leading forward, with two goals to go with eight score involvements.
Rising Kangaroos star Harry Sheezel fell five possessions short of 30. Had he done so, he would have been the first player in AFL history to reach that milestone in each of his first three matches.
ABC/AAP