Entering the Friday night blockbuster with a perfect 9-0 record at the 'G this year, the Demons were destroyed by the Cats' powerful seven-goal second quarter.
The second half was a stalemate after Geelong led by 20 points at the main break, the Cats always responding to the Dees' challenges to secure a vital win - 18.9 (117) to 14.13 (97).
In the absence of injured star Jeremy Cameron, key forward Shannon Neale put through four first-half goals and seemed set for a career-best bag.
Neale finished with five goals, but recalled forward Ollie Henry stepped up with four to justify his late promotion when key defender Sam De Koning was pulled out of the squad with illness only an hour before the match.
Oliver Wiltshire also had a significant cameo, kicking three goals, including dribbling the sealer through with six minutes remaining.
After losing five out of six games, the Cats have managed to defy crucial injuries to beat St Kilda and Melbourne to keep themselves in the hunt for a top-six finish.
"I thought we were just comprehensively outplayed early in the game, and it looked bad, to be honest," Cats coach Chris Scott said.
"They basically had everything they want, and we couldn't get the game on our terms.
"It was four goals to two, but it felt like 10 goals to two because they missed some shots."
Already without Cameron, Cats' star midfielder Max Holmes hurt himself last week against the Saints and could miss the rest of the home-and-away season.
But the likes of Tom Atkins and Tanner Bruhn stepped up to help Bailey Smith in the middle to combat Melbourne captain Max Gawn's impact on the game.
After signing on to play again in 2027 earlier on Friday, captain Patrick Dangerfield had to battle through pain after hurting his adductor in the second term.
Dangerfield soldiered on to finish with 12 possessions, but never looked convincing in his body and continued to receive heavy treatment whenever he was on the bench.
The Cats veteran also finished with ice on his calf after copping a knock to his shin.
Demons young gun Latrelle Pickett was ruled out with concussion after suffering an accidental elbow to the head late in the third quarter.
His cousin, Kysaiah, lit up the game early with a stunning goal that was followed by a Cristiano Ronaldo celebration, but the Demons superstar (14 possessions) had a tough night due to the attention from Geelong tagger Oisin Mullin.
Harrison Petty, on return from injury, booted four goals in a commanding display up forward for Melbourne.
Premiership forward Bayley Fritsch was also back to his best with three majors, but the Dees wasted numerous opportunities due to players not giving the ball off to teammates in better areas.
Melbourne will remain in sixth, but the result cost them a chance to maintain  pressure for a top-four spot.
"It was 101 points we gave them from turnover," Demons coach Steven King lamented.
"It was hard to get any flow in the game when we handed them that much ascendancy and rolled out the red carpet the other way.
"I'm not sure if it was Geelong's pressure at times, but some of our decisions and execution was pretty poor."
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