After two-straight defeats, the Cats appeared to be cruising to a convincing victory when they led by 29 points early in the second quarter.
But Geelong had to fight through a sloppy performance and a desperate Melbourne team who lifted their intensity significantly, but were again found lacking for polish and confidence.
Bayley Fritsch missed a gettable set shot two minutes into the final term when the Demons trailed by just 16 points, but Geelong made the Melbourne forward pay en route to a scrappy 12.13 (85) to 6.10 (46) victory.
On a night when most players were below their best, Dangerfield starred in his 341st AFL game.
He was Geelong's most dangerous forward as he kicked a goal in each of the first three quarters, but still proved valuable in the midfield.
Young midfield star Max Holmes was kept quiet by Melbourne's Tom Sparrow.
Geelong were dealt a major blow midway through the second quarter when premiership defender Jack Henry hobbled from the field with a right hamstring injury.
The Cats had only just brought star Tom Stewart back into the team, although he seemed still troubled with a knee issue that ruled him out of last week's defeat to the Brisbane Lions.
For the third week in a row, Geelong pulled a late change, with versatile tall Mark Blicavs out with an apparent illness and replaced in the team by veteran ruck Rhys Stanley.
It was a slightly improved performance from the Demons after heavy defeats to North Melbourne and Gold Coast.
But it was a similar tale for winless Melbourne, as they butchered the ball when going inside 50.
Star Christian Petracca was lively early up forward, kicking the Demons' first two goals.
But their struggles up forward were laid bare, continuing an alarming trend that has been a constant since their 2021 premiership.
Geelong have just six days until they open Gather Round with a monster clash with Adelaide, while the Demons (0-4) will be out to snap their losing streak when they take on Essendon.
