Demons foundation player Paxy Paxman put them in front for the first time since the opening quarter, with a snapped goal late in the frenetic last term on Saturday at Ikon Park.
Geelong's Chloe Scheer, who was sidelined for 2024-25 through injury, then marked in front of goal with 20 seconds left. It was a bread-and-butter kick for Scheer, but her shot went wide and the Demons won 8.8 (56) to 8.4 (52).
Melbourne twice fell 28 points behind in the third quarter, but they kicked the last five goals of the game in front of 4743 fans.
Stinear had coached Melbourne since the start of the AFLW, including their 2022 premiership, and this was the first time they played against him since he went to Geelong at the end of last season.
"This is a huge step in the right direction. More than anything, it's that momentum piece we're ticking off," Demons defender Tahlia Gillard said when asked about the significance of the win.
"To get back on top, that's something we can take away and bring into games coming up. Finals is all about momentum."
Stinear said the Cats tightened up after halftime and that Scheer was not to blame for the loss.
"We nearly escaped with a win, but I didn't feel like we'd earned it with our second half," Stinear said.
"From a team perspective, it shouldn't have come to that (Scheer's shot on goal).
"The outcome of the game is not on her, it's on us."
Despite trailing by 22 points at halftime and the dominance of Cats star Georgie Prespakis in the middle, Demons coach Tom Wilson was confident they could rally.
"I liked the way the game was looking," Wilson said.
Olivia Purcell and Tyla Hanks, in her 100th game, lifted in the midfield as Melbourne worked back into the contest.
Key forward Tayla Harris only had 14 possessions, but her second half was massive, and Cats star Nina Morrison briefly had to leave the field in the final term after Harris collected her with a brutal tackle.
After some errors earlier in the game, Demons forward Alyssa Bannan kicked the first two goals of the final quarter.
Then Paxman drifted into attack from the midfield and snapped what turned out to be the match-winner.
"She's been there since the start, hasn't she? Pax - a lot of experience - I reckon in finals, experience is really important," Wilson said.
Prespakis and Purcell ended up with 34 possessions apiece, with the Geelong star just in front for best-afield honours.
Geelong will now host the winner of Sunday's Sydney-Western Bulldogs elimination final next weekend in a semi-final at GMHBA Stadium.
The start of the game was delayed for 10 minutes because of a lightning warning. Typical of Melbourne's spring weather, it was sunny for most of the match, although a swirling breeze made conditions tough.
Geelong's Piper Dunlop (back) and Melbourne player Saraid Taylor (ankle) were able to play out the game after having to leave the field.
The Cats' Kate Surman will come under video scrutiny for front-on contact with Bannan on the wing in the third term.
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