In a scrappy, high-pressure contest at Victoria Park, Melbourne star Alyssa Bannan teed up skipper Kate Hore to deliver a six-point lead with two minutes left.
Imogen Barnett missed a late chance to tie the game, then after the siren Grace Campbell hit the post with a would-be match-winner, delivering Melbourne a 5.7 (37) to 4.9 (33) win.
"I just said to the girls: 'where are the cops? We just got away with absolute murder there'," Hore told the Seven Network.
"But we'll take it. A win's a win in this competition, you've got to keep banking them."
Both teams had their fair share of absences, with the Demons clearly missing the class of Olivia Purcell (ACL), Sinead Goldrick and Blaithin Mackin amid a lengthy injury list.
The Magpies were without skipper Ruby Schleicher (concussion), while Jordyn Allen (calf) and Bri Davey (ankle) are yet to return.
Brit Bonnici (27 disposals, six clearances, 10 tackles) and Carly Remmos (24 disposals) were prolific, while Tarni White was superb in defence.
Paxy Paxman (21 disposals) had an entertaining duel with Sarah Rowe (25 disposals) on the wing, while Maeve Chaplin (21 disposals, 11 tackles, 532 metres gained) was excellent.
Eden Zanker and Tayla Harris offered plenty of aerial presence.
Under relentless pressure from Collingwood, the Demons lacked composure but led by 13 points early, then eight at quarter-time.
Melbourne were held goalless in the second term, and Victoria Park erupted when Remmos put the Magpies in front in the third quarter.
But Hore (21 disposals, two goals) stepped up and snapped a crucial goal against the run of play to restore a one-point lead midway through the quarter, then turned provider for Georgia Gall.
The Demons led by four at three-quarter time and Collingwood spurned three good chances to regain the lead early in the final term.
With just over two minutes left, Bannan took a ripping contested mark then hit up Hore in the goal square.
"I've had a few go through the hands today, so it was nice to clunk that one," Hore said.
She kicked the goal, then watched as Collingwood almost pinched the four points back.
The Demons (3-0) next play Richmond at Casey Fields on Saturday, before Collingwood (1-2) face North Melbourne at Arden Street Oval on Sunday.
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