Down by eight points in the second quarter, Sydney slammed through nine goals in a row on their way to a 26.11 (167) to 10.10 (70) win at the SCG on Saturday.
Trailing 5-1 in centre clearances after the first term, the Swans fought back to score 58 points from that source, their highest in a decade.
"We just had to keep showing up at the contest, get a bit tighter at stoppage as well," Swans midfielder Errol Gulden told AAP after amassing a game-high 39 disposals.
"We were leaking from stoppage, so as mids (midfielders) we had to focus on getting to a body at stoppage and try to nullify their mids a little bit more and working back hard to help us start our ball movement.
"We've got full belief in our team, that even if we don't start well we can wrestle momentum back and over four quarters our game plan will stand up."
Curnow boosted his league-leading goal tally for the campaign to 62, was one of 12 Sydney goalkickers and had the better of his duel with former Swans defender Aliir Aliir.
"To have the impact in the air he did was great to see, he's been in really good form of late," Sydney coach Dean Cox said of Curnow.
Tom Papley, Jake Lloyd, Logan McDonald and Chad Warner all booted three majors as the home side registered their biggest score and win over Port, who slumped to a fifth-straight defeat.
The Power started well, winning inside 50s, contested possessions and clearances in the first quarter, which ended with them holding a two-point lead.
Mitch Zadow increased that advantage to eight by converting a set shot after Tom McCartin hit him high, but that was a good as it got for the visitors.
Sydney's improved centre bounce work generated more offensive opportunities and their classy midfielders fed their forwards with several pinpoint kicks.
The lead blew out to 50 before Port kicked the last goal of the second quarter to trail by 46 at halftime.
The Swans kicked four goals to one to hold a handsome 59-point advantage at three-quarter time and ten to four in the last.
"We're not going to sit here and feel sorry ourselves at losing by 97 points, we're disappointed with that, but the bigger picture is a lot bigger than that," Port coach Josh Carr said.
Jack Whitlock booted three goals and Jason Horne-Francis two for the Power, though the latter hyperextended a knee in his 100th game.
"We were a little bit worried about it, but he's looking OK, from all the tests it's looks fine," Carr added.
Jase Burgoyne had 34 disposals and seven clearances and Willem Drew accrued 31 touches and nine clearances.
