The Giants got out to a game-high 25-point lead at the start of the third quarter and appeared on track for a second win of the season, before Prespakis kicked into overdrive and the Bombers lifted their pressure.
The star on-baller racked up 13 disposals, six contested possessions, three clearances and a goal in the third term to put Essendon on her back and inspire a terrific 6.7 (43) to 5.5 (35) comeback at Henson Park on Saturday afternoon.
"Genuinely just so proud of the resilience of the group," skipper Bonnie Toogood told Fox Sports.
"And it's been a challenging season, I suppose, and the persistence through adversity, particularly today.
"The first half wasn't what we were planning on, but to come out in the third like we did and just big moments by individuals - bloody inspiring."
The victory relieves some pressure on Bombers coach Natalie Wood and leaves St Kilda as the league's only winless team.
It was a devastating loss for Cam Bernasconi's GWS, who kicked five of the first six goals then only scored one point in a second half where they were completely overwhelmed by Essendon's manic pressure.
Essendon had trailed by just four points at th final change when star forward Toogood gave the Bombers a massive rev-up at the huddle.
"I'm passionate and emotional all the time - it could be the Italian in me," Toogood said.
"They were on the back foot ... I was like 'we've got 'em - lean into that, we've got them, our football is working'."
Essendon hit the front when they went from end to end and Daria Bannister tumbled home a long-range goal.
Then Emily Gough kicked a terrific checkside from a forward-50 stoppage that sealed victory.
Prespakis finished with a mammoth 35 disposals and five clearances, and she was well-supported by Maddi Gay (21 disposals) and Georgia Gee (15), along with ruck Steph Wales (20 disposals, 14 hitouts, eight clearances).
Skipper Bonnie Toogood (eight marks, one goal) and Emily Gough (two goals) were influential in attack, while Alex Morcom and Amy Gaylor (nine intercepts apiece) were strong down back.
The Giants' best were Alyce Parker (25 disposals, eight tackles, two goals), Tilly Lucas-Rodd (26) and Cambridge McCormick (22).
Essendon (16th, 1-7) face the finals-chasing Western Bulldogs at Whitten Oval on Friday, while GWS (15th, 1-7) have a daunting task of facing red-hot Geelong at GMHBA Stadium next Saturday.
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