The Cats dominated the first three quarters and were 63 points up when Joel Selwood booted his fourth goal four minutes into the final term.
But the Power narrowed the final margin by kicking six unanswered goals in the last 23 minutes.
Chris Scott's men looked relieved when the final siren sounded, signalling a 20.9 (129) to 16.8 (104) win for the home side.
It was Geelong's 15th victory of the season and its ninth consecutive defeat of Port Adelaide, a streak which dates back to round 21, 2007.
The result keeps the Cats within four points of ladder-leader Hawthorn with three home and away games to come.
Keen to see his team atone for its loss to North Melbourne last weekend, Scott had plenty of headaches early on, with Mitch Duncan suffering concussion after a big tackle from Jackson Trengove just five minutes into the first quarter.
Duncan was temporarily subbed out to be assessed and was permanently taken out of the game before the end of the opening term.
But as Duncan put on the red vest, his teammates hit top gear. They were 31 points up at quarter-time and extended their lead to 51 at the long break.
Steven Motlop led the way in the midfield for Geelong, using his pace and creativity to amass 12 disposals in the opening quarter. He finished the match with 22 disposals and two typically brilliant goals.
Triple premiership players Steve Johnson (32 disposals) and Joel Corey (29 touches) were the other leading ball-winners.
Selwood led the way on the scoreboard with a career-high haul of four goals, while Harry Taylor, who spent time at both ends of the ground, ended the game with three.
Down back, Corey Enright did a great blanketing job on Power dynamo Chad Wingard, holding him to just one goal.
With Wingard unable to repeat his Showdown heroics, small forward Angus Monfries stepped up in impressive fashion, notching a new career high by kicking seven goals.
Skipper Travis Boak (30 touches) and big man Matthew Lobbe were Port's other leading lights.
Lobbe, who tallied 59 hit-outs, had the better of Geelong's inexperienced rucking duo of Nathan Vardy and Josh Walker.
The Power remain eighth, although their loss keeps Carlton very much in the hunt for a finals berth.
Ken Hinkley's men host Gold Coast at AAMI Stadium next Saturday afternoon.
The Cats travel to Perth next weekend for a Saturday night meeting with West Coast at Patersons Stadium.
GEELONG 6.4 12.7 19.9 20.9 (129)
PORT ADELAIDE 1.3 4.4 10.5 16.8 (104)
GOALS
Geelong: Selwood 4, Taylor 3, Podsiadly 2, Christensen 2, Motlop 2, Bartel, Hawkins, Varcoe, Guthrie, Caddy, Kelly, Walker,
Port Adelaide: Monfries 7, Schulz 2, Boak, Gray, Ebert, Lobbe, Colquhoun, Wingard, Moore
BEST
Geelong: Selwood, Motlop, Enright, Corey, Taylor, Mackie
Port Adelaide: Boak, Lobbe, Ebert, Monfries, Pittard
INJURIES
Geelong: Duncan (concussion)
Port Adelaide: Nil
SUBSTITUTES
Geelong: Jesse Stringer replaced Mitch Duncan (concussion) in the first quarter
Port Adelaide: Kane Mitchell replaced John Butcher in the third quarter
Reports: Nil
Umpires: Rosebury, Ryan, McInerney
Official crowd: 24,784 at Simonds Stadium
