It was the Power's inaccuracy in front of goal that proved the difference between the two sides.
The Power was determined to make amends for its disappointing six-point loss last week and showed it had regained its fast-running game.
Port Adelaide was hard at the ball from the first bounce and, as with the Round 13 match against the reigning premiers at the SCG, battled the Swans for supremacy early in the first term.
The Power matched the Swans for pressure around the ball and went into the the first break with a narrow one-point lead.
Jack Hombsch had the tough job on Lance Franklin and had the upper hand on the star forward in the first term, holding him to just one behind.
Despite a momentum swing towards Sydney on the back of two goals to Franklin, the Power continued to push forward through Robbie Gray and skipper Travis Boak.
The Swans went on to boot three more goals to the Power's one through Matt Lobbe.
Port Adelaide had a chance to go into the main break just five points behind, despite Sydney's control of much of the second term, but a free kick to McGlynn and a goal on the half time siren gave the Swans an 11-point buffer at the main break.
Port Adelaide maintained its intensity and pressure around the ball, forcing the Swans into skill errors, but could not capitalise on its opportunities when in possession and the Swans got out to a 22-point lead midway through the third quarter.
Travis Boak provided a glimmer of hope for Port during the term by booting two goals to help keep the Power just 15 points short at the final change, but Sydney's pressure and slick ball movement was too good.
Port Adelaide next travel to Metricon Stadium where it will take on the Gold Coast Suns on Saturday 16 August.
SCOREBOARD
PORT ADELAIDE 2.3 3.7 5.12 7.16 (58)
SYDNEY SWANS 2.2 5.6 8.9 12.12 (84)
PORTADELAIDEFC.COM.AU'S BEST
Boak, Hombsch, Gray, Ebert, Broadbent
GOALS
Boak, Neade 2, Wingard, Westhoff, Lobbe
INJURIES
Nil
REPORTS
Nil
CROWD
50,087, at Adelaide Oval
