Daicos (39 disposals, one goal) helped the Magpies overturn a 27-point second-quarter deficit in a stirring 16.12 (108) to 11.8 (74) triumph on Thursday night.
Collingwood extended their winning streak to six games and climbed to seventh on the ladder.
Adelaide great Taylor Walker kicked his 700th career goal, but the fifth-placed Crows blew a chance to rise to third spot.
Adelaide held a 27-point lead 15 minutes into the second term, when Walker had already booted three majors.
But the Magpies climbed from the canvas in style, scoring 13 of the next 16 goals to stun the 50,109-strong Adelaide Oval crowd.
"You come over to Adelaide and play a team that's arguably the top four teams in the competition based on form ... to put 108 points on the board is pretty significant," Collingwood coach Craig McRae said.
"It's probably beyond my expectations."
Daicos was instrumental, as were ruckman Darcy Cameron (23 disposals, six clearances, 37 hitouts) and veteran Scott Pendlebury (29 touches, one goal).
Magpies Dan McStay, Tim Membrey and Ed Allan kicked two goals each, and defender Isaac Quaynor (20 possessions) - the victim of Izak Rankine's vilification last season - and 200-gamer Jordan De Goey (20, one goal) were also standouts.
Adelaide's Walker couldn't add to his early three goals while Riley Thilthorpe also finished with three.
Crow Sam Berry collected 30 disposals and 10 clearances, Rankine - facing the Pies for the first time since his homophobic slur suspension - had 25 touches, and defenders Wayne Milera (24 possessions) and Josh Worrell (21, seven marks) were busy.
Collingwood kicked the initial two goals before a rapid retort from the Crows, who scored five goals in 15 minutes including Walker's landmark.
The 36-year-old threaded a 45-metre set shot from a boundary line to become the 28th VFL/AFL player to reach the 700 goal milestone.
Walker soon added another to help the Crows to a 13-point lead at quarter-time, 5.3 to 3.2.
The Adelaide great kicked his third major early in the second quarter, Thilthorpe converted, and the home side were 27 points clear.
But the Magpies rallied late, turning the tide with three quick goals including a stunning long-range checkside effort from McStay, that reduced their halftime deficit to just eight points.
"It was like we just stopped," Crows coach Matthew Nicks said.
"And when you give a team momentum, we weren't able to bring that back."
The Collingwood onslaught continued in the third quarter, with De Goey kicking one of four Magpie goals to Adelaide's two as the visitors created a 14-point lead.
Crow Ben Keays pegged one back late to shrink the margin to eight points at three quarter-time.
But Daicos then put an exclamation point on his superb display, converting a long bomb on the run for the opening goal of the final term as the visitors finished with flourish.
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