The Power shocked their hosts with eight first-quarter goals in a stunning early blitz to lay the platform for their 15.11 (101) to 14.11 (95) triumph on Friday night at GMHBA Stadium.
They led by as much as 49 points during the second quarter before Geelong mounted a serious response, cutting the margin back to one straight kick late in the final term.
There was last-gasp drama as Jeremy Cameron was denied a goal on the line when play was called back for a free kick to Ollie Henry, who snapped a behind from the pocket.
It was the final score of the game as undermanned Port - missing skipper Connor Rozee among four injury-enforced changes - held on for their first win at Kardinia Park since 2007.
Acting captain Zak Butters stood up for Port in the absence of injured skipper Connor Rozee. (Julian Smith/AAP PHOTOS)
The result gave the Power a 6-3 record ahead of a home clash with Hawthorn next week, while Geelong (7-2) have lost successive games after opening the campaign with seven straight wins.
Willie Rioli equalled his career-best haul with four goals for Port as Ollie Wines (33 disposals, nine clearances) and acting captain Zak Butters (34, seven) stood up in Rozee's absence.
Jason Horne-Francis (26 touches, seven clearances) was best afield in the first half before Geelong substitute Oisin Mullin quelled his influence after the main break.
Former Geelong defender Esava Ratugolea held ex-teammate Hawkins to just seven touches as the veteran forward matched Joel Selwood's games record for the Cats.
Hawkins ended his unprecedented four-match goal drought with a second-quarter major but put another set shot out on the full.
Tom Hawkins ended on the losing side in his record-equalling 355th game for the Cats. (Julian Smith/AAP PHOTOS)
Defender Zach Guthrie (24 disposals), Tyson Stengle (four goals) and roaming forward Cameron (18 touches, one goal) were among the Cats' best.
Geelong gave up a 25-point head-start in the opening nine minutes and conceded the highest first-quarter score to a visiting team at Kardinia Park since 1983, trailing 8.2 to 3.3 at the first break.
The Power added the first three goals of the second term before desperate Cats coach Chris Scott replaced ruckman Rhys Stanley with Mullin.
Hawkins and Gryan Miers booted successive goals to temporarily stem the tide but Butters' superb snap helped Port to a 41-point lead at the main break.
The Cats kicked six goals to two in the third term, with defender Guthrie taking advantage of twin 50m penalties against Rioli to kick a rare major.
Gary Rohan pulled down a spectacular grab with a ride on Ratugolea's back in the final term and Stengle's fourth major cut the deficit to seven points before Henry missed with the last shot of the game.
