Two days after the Swans won through to the AFL grand final, Cynthia Hamilton laid a crucial tackle inside the last minute and they held on 6.7 (43) to 6.4 (40).
Three goals were kicked inside the last two frenetic minutes at Henson Reserve on Sunday, with Sydney posting their second win of the AFLW season.
It is the second straight week that the Giants have been able to secure a close win, following last week's last-gasp draw with Gold Coast.
Hamilton had a big last term, kicking the first two goals to put Sydney up by 15 points after eight minutes.
But Zarlie Goldsworthy, who had to leave the field in the third term after she was crunched in a marking contest, kicked a goal three minutes later to keep it interesting.
Goldsworthy's accurate snap inside the last two minutes made it a three-point game.
An outstanding clearance by Montana Ham at the next centre bounce found Aimee Whelan, who marked and kicked what turned out to be the match-winning goal.
With 40 seconds left, Brodee Mowbray marked and goaled to bring the Giants back to within three points.
Then Eilish O'Dowd tried to break clear for GWS at the final centre bounce, only for Hamilton to lay her game-saving tackle.
Hamilton won a holding-the-ball free and Sydney ran down the clock for the win.
Laura Gardiner starred for the Swans with a game-high 32 possessions, while Sarah Grunden kicked her first two AFLW goals in the opening term to help spark Sydney.
Hamilton also finished with two goals, as did Goldsworthy and fellow Giant Alcia Eva.
Bec Beeson racked up 10 clearances for GWS in her 25-possession game, which also featured 428 metres gained.
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