Cheekily declaring "We are the Pies of South Australia" on their banner, Collingwood broke clear in the second term and were in control for much of the game, winning 16.13 (109) to 12.6 (78) in front of 47,649 fans.
With Dan Houston suspended and Jordan De Goey and Lachie Schultz injured, the Magpies could have been vulnerable.
But Jamie Elliott and Beau McCreery stepped up superbly in attack, while veteran Steele Sidebottom and fellow midfielder Ned Long were prolific as Collingwood stormed to their fourth straight win.
It sets up a massive clash at the Gabba next Thursday night, when Collingwood take on reigning premiers Brisbane.
Captain Darcy Moore led an ironclad Collingwood defence that shut down the Swans, who had impressed in last week's emphatic win over North Melbourne.
As expected, Swans tagger James Jordon kept Collingwood star Nick Daicos company for much of the night and went some way to quelling his influence in the first half.
But the younger Daicos worked his way into the match and racked up a game-high 34 disposals.
Collingwood's Darcy Cameron won his ruck duel against Brodie Grundy, who had been influential early.
Collingwood's banner was a dig at the theme song of the Crows and also at Port Adelaide, who are the Magpies in the SANFL.
After an even first term, Collingwood had a six-minute purple patch early in the second that yielded four goals.
Had a Brody Mihocek snap not been touched by a desperate Swans defender, the Magpies would have broken out to a 30-plus lead.
Instead, Sydney responded with a three-goal burst that brought them back to within nine points.
Then Elliott's excellent roving of the pack gave Collingwood the last goal of the half and they led by 17 at the main break.
Adding to Sydney's issues, they lost key forward Joel Amartey in the second quarter to a hamstring injury.
Mature-age recruit Riley Bice, the focus of attention after his excellent game last week against North, was again setting up Sydney attacks with his long passes off half-back.
But too often the Swans' system broke down under relentless Magpies pressure.
Collingwood broke out to a game-high lead of 32 points in the third quarter before Sydney brought it back to 25 at the last change.
Swans star Isaac Heeney played something of a lone hand, with 28 possessions and two goals.
Elliott and Mihocek kicked three goals apiece and McCreery added another two, while Sidebottom had 28 possessions.
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