After Carlton suffered a 34-point loss to the Demons earlier on Saturday, the Swans (5-1) knew a win at Alberton Oval would move them four points clear of their fifth-placed rivals.
Molloy was instrumental in helping them secure the precious 5.11 (41) to 3.9 (27) victory, booting a trio of goals to register her third consecutive match in which she has kicked three or more majors.
Her dazzling display (15 disposals) came despite the Power keeping Sydney's usually dynamic attack at bay in the first half, the scores locked at 16-16 at the main break.
The visitors stepped up in the third quarter, with Molloy booting a crucial goal, although a late major by Gemma Houghton kept Port in the contest.
Leading by four points at three-quarter time, young Swans forward Cynthia Hamilton snagged a settling major, before Molloy booted another to open up a match-winning advantage.
Sydney defender Zippy Fish was typically influential, picking up 26 disposals, while midfielder Montana Ham had 16 possessions.
Midfielder Abbey Dowrick was a shining light for the Power (2-4), racking up a game-high 27 disposals and 415 metres gained.
Elsewhere, the Western Bulldogs may have scored just one point in the first and third quarters combined, but they held firm to claim a 6.4 (40) to 4.6 (30) victory over Fremantle.
Looking to jump into the top eight, the Bulldogs (4-2) were kept scoreless in the opening term at Cockburn ARC Oval, but kicked four unanswered majors in the second to lead by 11 points at the main break.
Fremantle tightened their defence in the third quarter, holding the visitors to just one point as they surged back after Hayley Miller and Kiara Bowers found goals.
But just 17 seconds into the final quarter, a series of slick handballs led to Bulldogs forward Heidi Woodley slotting a major, before Sarah Hartwig nailed a goal to help her team move up to seventh on the ladder.
The Dockers (3-3) missed an opportunity to cement themselves inside the top eight, although Bowers (23 disposals, eight tackles, one goal) was busy, while midfielders Gabrielle Newton and Aisling McCarthy posted 24 possessions each.
Defender Jess Fitzgerald (25 disposals) shone for the visitors, and midfielder Isabelle Pritchard jagged 21 disposals and a goal.
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