Ollie Henry kicked a career-high four goals and Gryan Miers was creative forward of centre in the 14.13 (97) to 12.13 (85) victory at GMHBA Stadium on Saturday night.
It put the Cats back into the top eight on percentage ahead of Carlton, who have a game in hand.
Off-season recruit Henry starred early, with four goals to his name by the opening minutes of the second quarter, while Miers (24 disposals) kicked two goals and had a direct hand in five others.
Experienced guns Isaac Smith (22 disposals, one goal) and Patrick Dangerfield (20, one) were also influential and key defensive pair Tom Stewart and Esava Ratugolea stood up in defence.
Port Adelaide's fourth straight defeat left their top-two spot in jeopardy and came amid a raft of injuries and illnesses.
The Power made six forced changes, with Jeremy Finlayson and Miles Bergman (both illness) late withdrawals before losing Trent McKenzie to a knee injury in the opening 10 minutes.
It got worse when Todd Marshall, crucial in the absence of fellow tall forwards Finlayson and Charlie Dixon (foot) and Finlayson, jogged off before quarter-time after hitting his head on the ground in a diving attempt to mark.
Power officials had come under intense scrutiny over their botched management of Aliir Aliir's concussion protocols and took no risks with Marshall, sending him downstairs for further assessment.
Marshall was cleared to return and kicked a pair of important goals from strong marks either side of three-quarter time.
The second put Port in front early in the final term but Geelong finished stronger, kicking four of the last five goals.
Midfield stars Zak Butters (30 disposals, one goal) and Connor Rozee (27 touches) were brilliant for Port and Willie Rioli finished with four goals, while Sam Powell-Pepper kicked three.
Both sides took advantage of perfect conditions in a free-scoring first quarter as Rioli and Henry booted three goals apiece.
Henry's third sailed through after the quarter-time siren to give the Cats a 44-31 lead at the first break.
Henry's purple patch continued with the first goal of the second term and Geelong extended their advantage to 17 points by halftime.
A brilliant Powell-Pepper snap sparked Port early in the third quarter and they gained confidence as they piled on four goals to one for the term.
Marshall put them in front and the lead changed hands six times before the Cats won the arm wrestle between two desperate sides in a tough final quarter.
Jeremy Cameron kicked two goals for Geelong and Mitch Duncan (one) was important in attack.
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