Geelong trailed by seven points at three quarter-time but triumphed 16.10 (106) to 14.10 (94) in a wildly swinging affair at Adelaide Oval.
The defeat leaves Port on the brink - they're in 11th spot, six premiership points behind eighth-placed Richmond with four games remaining before the finals.
But the Cats retain top spot after Hawkins scored two clutch goals - with four and three minutes remaining respectively - the final two scores of the thriller.
Geelong defender Zac Tuohy collected a game-high 27 disposals, his teammates Tom Atkins and Cam Guthrie both had 24 touches and Jeremy Cameron kicked three goals.
Geelong led by 34 points at halftime but Port's Charlie Dixon triggered an astonishing third-term comeback as the hosts booted eight goals to one.
Dixon scored two goals and took five marks in the quarter to revive the Power, who were well-served by Mitch Georgiades (three goals), Sam Powell-Pepper (19 disposals, two goals) and Karl Amon (25 possessions, one goal).
But the Cats rallied with four goals to one in a tense last term - scores were tied in the 16th minute when Port's Amon goaled, before Hawkins' late heroics.
Geelong edged to a four-point lead after a fast-paced opening quarter and then accelerated in a second-term blitz, booting six goals to one.
The Cats lost ruckman Rhys Stanley to a knee injury but led 11.3 to 5.5 at halftime.
Dixon inspired a Power comeback as the home side scored eight goals to one in a stunning third quarter.
Port led by seven points at three quarter-time after Dixon's brilliant quarter - he booted two goals from 11 disposals, took five marks, had two score assists and two inside 50s in the term.
But Geelong spearhead Cameron slotted his third goal just 13 seconds into the last quarter and the Cats finished with a Hawkins flourish to bank their 14th win of the season.
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