Less than two hours after Collingwood ended Sydney's perfect start to the season on Saturday, the Power did the same to Melbourne with their 6.7 (43) to 5.11 (41) upset.
Melbourne's Megan Fitzsimon had a snap at goal with a minute left, but her kick went wide for a behind and the Power were able to close out the game.
Indy Tahau, who resumed this season after 695 days out with a knee reconstruction, was massive for Port with three goals.
Melbourne captain Kate Hore also kicked three goals and was best afield, putting the team on her back as she tried to lead them to a comeback win.
The Demons won several team statistics - they had 73 more possessions, led inside-50s 43-30, and had three more scoring shots.
But the Power were more efficient in attack and their pressure was outstanding, winning the tackle count 81-64.
Melbourne kicked three goals to one in the final quarter, and Hore's third from a contentious free kick brought them to within three points with less than two minutes left.
It came a week after West Coast overwhelmed Port in the last quarter, storming home for the win.
But this time the Power were able to hold on and take their record to 2-3.
Melbourne are 4-1, leaving premiers North Melbourne and Hawthorn as the only unbeaten teams.
Those leaders face massive games on Sunday, with Hawthorn hosting Adelaide, and the Kangaroos in Brisbane for their grand final rematch against the Lions.
Ella Boag kicked the only goal of the first quarter on Saturday, and keeping the Demons to four behinds was a big early win for the hosts.
Gemma Houghton and Tahau then put Port 17 points up in the second, before Hore kicked a badly needed goal for the Demons at 14 minutes, and the margin was nine points at the main break.
Tahau's second and a goal to Chloe Gaunt gave Port a game-high lead of 23 points in the third term.
Then - who else? - Hore stepped up to kick Melbourne's only goal of the quarter.
When Ryleigh Wotherspoon kicked a goal a minute into the last quarter, Melbourne were only 11 points down.
But Tahau's third gave Port crucial breathing space as Tayla Harris and then Hore brought the Demons roaring back.
Hore had the complete game - 27 possessions including 13 contested, nine tackles and seven clearances, along with her three goals.
Port's Abbey Dowrick racked up a game-high 12 tackles as well as four clearances and 12 contested possessions, while Matilda Scholz had 19 hitouts and took five marks.
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