Trailing by 21 points in the second term on Friday night, the Cats reduced the margin to three points at the main break, then kicked 10 goals to six after halftime for the 14.23 (107) to 11.8 (74) victory.
Skipper Patrick Dangerfield led the way with five goals in front of a crowd of 96,680, the biggest for an AFL match at the MCG this season.
Chris Scott's Cats next head to Optus Stadium to face minor premiers Fremantle, who suffered a demoralising qualifying loss to Hawthorn on Thursday night.
For Carlton, it brings an end to a magnificent fightback under coach Josh Fraser from a 1-8 start to the season that cost predecessor Michael Voss his job, to a 10th-place finish, a wildcard win and an elimination final berth.
The Blues only lost three of 16 games under Fraser, winning 12 and drawing another.
Geelong midfielder Shaun Mannagh (25 disposals) was wonderful, while Dangerfield's five goals and 10 score involvements from 20 disposals were pivotal.
Gryan Miers (24 disposals, two goals) and Oli Wiltshire (22) were influential, while Bailey Smith (25) fought through Cooper Lord's tag.
On his return from injury, Max Holmes was used in bursts by the Cats.
Tom Stewart had 11 intercepts and Connor O'Sullivan blanketed Harry McKay.
Carlton defender Jacob Weitering was magnificent, while Sam Walsh (29 disposals), George Hewett (27) and Patrick Cripps (12 clearances) fought hard.
Frank Evans kicked two goals and Billy Wilson (26 disposals) was busy.
Carlton started fast in teeming rain, smashing Geelong at clearances 10-4 and outnumbering the Cats all over the ground.
A highlight was Cripps' wonderful snap off the outside of his boot from the pocket as the Blues snatched a 13-point lead at quarter-time.
Young Blue Harry Dean copped an accidental boot to the face from teammate Lewis Young after a marking contest, but passed his head injury assessment (HIA) check.
Miers and Brad Close helped Geelong creep closer to the Blues, before Holmes put the Cats within three points.
Mannagh put the Cats in front with their fourth goal on the spin at the start of the third quarter.
Carlton fought back and briefly regained the lead.
But the young Blues were simply overwhelmed by pure weight of numbers as the Cats got on a roll.
Dangerfield's second major kicked off a run of eight goals, and the decorated Cats skipper jagged two in quick succession in the final quarter to slam the door shut.
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