Gemma Houghton's massive goal with less than a minute left gave Port the lead for the first time on Sunday at Alberton Oval and they won 7.1 (43) to 6.6 (42).
Had Port lost, they would have been on the road next weekend in their first finals series to play Fremantle in one of the knockout matches.
Instead, the win in front of a boisterous home crowd of more than 4000 means they will host Richmond in their elimination final.
It was a brutal end to the season for the Giants, whose losing streak extended to eight games.
They were outstanding for much of the match, but the experience of Power veteran Kirsty Lamb was critical when the match was on the line.
Lamb snapped the opening goal of the final term and then her pass found Houghton, who marked and kicked the match winner.
Adding to the tough day for GWS, Meghan Gaffney suffered a right knee injury. She returned this season from an ACL rupture.
The Giants have averaged 70 tackles per game, but on Sunday they had a whopping 106 to 80.
GWS captain Bec Beeson was mighty, kicking their only goal in the last term and amassing a game-high 25 disposals in her best-afield performance.
She stayed on the ground in the frenetic last quarter despite a head knock.
Port's Maria Moloney was critical with her 17 disposals, including 13 contested possessions.
Port suffered a double blow pre-game when ruck Matilda Scholz (calf) and midfielder Abbey Dowrick (soreness) were late withdrawals.
GWS piled on the pressure from the start and were rewarded when Eilish O'Dowd kicked the opening goal after three minutes.
They held a game-high lead of 17 points in the third term, but Port kept with them and kicked three goals to one in the last quarter.
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