Separated by just two points by three-quarter time, the Swans snatched their first away win with a 6.9 (45) to 3.12 (30) victory at Alberton Oval on Saturday in a thrilling arm wrestle.
It was a far cry from the teams' maiden clash last season, in which the Swans scored only two behinds to lose by 66 to the Power.
Box office match-ups lit up the crowd, with rising stars Ally Morphett and Matilda Scholz facing off in the ruck as Port powerhouse Erin Phillips played on Sydney co-captain Chloe Molloy.
"We haven't been able to do that on the road. That's the first win," Molloy told Fox Footy.
"To Port Adelaide's credit, their crowds are awesome. You hear the 'Never Tear Us Apart' and we just silenced that."
Morphett took out the match with a game-high 21 hit outs, while Phillips worked overtime to keep Molloy goalless for the first three quarters.
The Swans enjoyed an even team performance across the field, complemented by a stand out display from Laura Gardiner (33 disposals, six clearances) in the midfield and Lucy McEvoy (11 intercept possessions), who was a brick wall in defence.
Cynthia Hamilton opened the scoring for the Swans but was upstaged by a terrific goal from Port's Gemma Houghton.
Scholz had sent a long bomb to an empty forward 50 as Houghton flaunted her speed to leave Alice Mitchell in the dust and grab the six points for the Power.
With the Swans leading by one point at quarter-time, Bec Privitelli and Bella Smith kicked back-to-back goals in less than two minutes as their lead extended to 18.
Two goals by Ash Saint kept the Power alive, but inaccuracy in front of the posts cost the hosts.
With just two points the difference going into the final term, Jaide Anthony put boot to ball to slot her first AFLW goal, while Molloy finally kicked her own major to grab a comfortable win for her side.
Sydney (3-3) return to Henson Park to host 15th-placed Hawthorn next round while Port Adelaide (1-5) face a formidable challenge against third-place North Melbourne at Arden Street.