The Saints appeared destined to secure their first points of 2023 when Jesse Wardlaw nudged their lead beyond three goals in the third quarter at RSEA Park on Sunday.
But Hannah Ewings and Indy Tahau kicked four goals between them to give Port Adelaide the edge, before skipper Erin Phillips nailed the sealer, her first goal in Power colours, for a 8.8 (56) to 7.6 (48) victory.
"We obviously had a really strong fixture in round one and two, playing the Crows and Lions," coach Lauren Arnell said.
"Just the response from the group and to get our first away win as an expansion team in our second season is really exciting.
"It's probably not just the result, it's the way we went about it. I'm really proud of the group."
Port Adelaide midfielders Phillips (20 disposals and six clearances) and Abbey Dowrick (24 touches, nine clearances, 567 metres gained) didn't stop while youngster Matilda Scholz and Tahau were a strong ruck combination.
St Kilda's Jaimee Lambert kicked two goals and racked up 16 disposals and nine tackles and was supported by Hannah Priest, Tyanna Smith and Olivia Vesely.
Port's Ashleigh Saint traded two early goals with St Kilda's Darcy Guttridge before Nicola Xenos put the Saints in front after Port were penalised for a deliberate out of bounds.
The Saints led by six points at halftime and after Lambert and Wardlaw goaled in quick succession, appeared on track to claim victory.
Instead, the Power kicked the next five goals.
Port's Janelle Cuthbertson and St Kilda's J'Noemi Anderson had to come off after a nasty head clash in the third quarter, with the latter concussed and unable to return.
Port Adelaide cut the deficit to five points before three-quarter time via a bizarre Tahau goal.
Tahau's running shot landed on the goal line and seemed destined to go through for a point before the ball bounced at right angles and hit the goal umpire.
After a discussion with the field umpire, it was ruled a goal.
Early in the final term, Ewings kicked an extraordinary goal to put the Power in front.
Tahau and Phillips struck to seal an impressive comeback win.
"We did a lot right, had some great structure behind the football in regards to our defenders, just made some poor decisions at critical moments that cost us goals," Saints coach Nick Dal Santo said.
"We've got work to do, there's no hiding that."
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