The Power were clinging to a one-point lead with less than eight minutes remaining in Saturday's match when Borg - scrambling on hands and knees while trying to collect the bouncing ball in the goal square - was adjudicated to have deliberately rushed the behind.
Borg and her teammates were left stunned by the controversial decision, with Geelong speedster Mikayla Bowen kicking the goal from point-blank range to give the Cats a five-point lead.
It ended up being the last goal of the match, with Port's late chance at forcing a draw - a flying shot on goal from Justine Mules-Robinson with less than 90 seconds remaining - being touched on the line.
The 6.9 (45) to 6.4 (40) win was Geelong's third victory on the trot, evening their season ledger to 3-3.
Port, who stunned Melbourne last week, are now 2-4 and face a huge battle to make the finals.
"I think right after the game is probably not the time for me to comment on it," Port coach Lauren Arnell said when asked about the controversial late umpiring decision.
"No doubt there will be some conversations about those types of decisions from today's game.
"But I'd prefer not to comment on that immediately post game."
In further heartbreak for the Power, the future of former captain Janelle Cuthbertson is in doubt after scans confirmed she had torn the ACL in her left knee for a second time.
The 35-year-old tore her ACL in round two last year, and she was on the brink of making her long-awaited return before suffering a repeat tear at training on Thursday night.
Cuthbertson is out of contract at the end of the season, and whether she will have the chance to play again at AFLW level hangs in the balance.
Port battled hard in Saturday's match, with Indy Tahua kicking two last-quarter goals to give her side a chance to nab victory, while Matilda Scholz (19 disposals, 22 hitouts, one goal) was huge in the ruck.
For Geelong, star midfielder Georgie Prespakis (24 disposals, six clearances, 568m gained) and Bowen (25 disposals, nine tackles, one goal) were the leading ball winners.
Geelong's Emma Kilpatrick suffered a first-half concussion after being crunched in a tackle by Port's Ebony O'Dea, while Julia Crockett-Grills injured her hamstring in the fourth quarter.
Prespakis ran riot in the first quarter with eight disposals, three clearances and 247m gained as Geelong went into the first break up 10-0.
Port made the most of the wind in a rainy second quarter, winning the clearances 9-3 on the way to kicking four goals to two to take a one-point lead into half time.
Power debutant Lauren Young, who endured two ACL tears on the way to realising her AFLW dream, showcased her potential with two important marks late in the second quarter.
Nina Morrison kicked the only goal of the third quarter, and there were a number of lead changes in the final quarter before the controversial free kick was paid against Borg.
