GWS coach Leon Cameron applauded the composure of match-winners Josh Kelly and Toby Greene, who nailed clutch goals to help their AFL club snatch a two-point SCG derby win.
Lance Franklin's five-goal haul, which earned him the Brett Kirk medal for best on ground, and the Giants' inaccurate goal-kicking looked set to extend Sydney's undefeated start to 2021 beyond Saturday's thrilling arm-wrestle.
GWS stand-in skipper Greene was the worst offender, finishing with seven behinds and one goal to make it the most inaccurate match of his 163-game career.
But it was Greene's goal, coming with three-and-a-half minutes remaining in the match, that put his side within striking distance after a flurry of wasted opportunities, near-misses and what-ifs.
With 66 seconds remaining, Kelly pounced on opposing ruckman Sam Reid's hitout then snapped truly from a tight angle to put his side in front for the first time since the opening quarter.
The Giants held on during a frantic final minute, triumphing 9.17 (71) to 10.9 (69).
Key defender Tom McCartin made decent connection with his attempt to kick an after-the-siren goal from beyond 60 metres, but it was always going to prove too much of an ask.
"With close games, you get a bit nervous," Cameron said.
"It was a fabulous spectacle for footy in Sydney.
"We were kicking poorly. We always believed we were in it, we just needed to nail our fundamentals.
"He (Kelly) played a really good game ... nailed the one we needed."
Cameron, who confirmed veteran Sam Reid tweaked his hamstring, noted Greene has already put his hand up for extra goal-kicking practice on Monday.
"It takes a special player to want big moments," Cameron said.
"He's a special talent, special player and led us from the front again ... he just never gives up and the players love it."
Kelly, who put an optimistic attempted match-winner out on the full prior to decisively roving the pack with aplomb, admitted he was "having a shocking kicking night".
The midfielder termed it a "bloody good game of footy" on Fox Footy, but Swans coach John Longmire was less enthused after ruckman Tom Hickey suffered a knee injury in the round-five upset.
"We stopped a bit in the last quarter, when they had 10 scoring shots," Longmire said.
"We couldn't get it done when it mattered.
"We just needed to pick him (Kelly) up - pretty key, pretty simple. Some good learning for a few of our younger fellas - and a reminder for some experienced players, we should have got it sorted."
GWS unsettled the Swans with praiseworthy pressure and dominated patches of the contest, making it four wins at the SCG from their past five visits.
It also meant back-to-back victories for Cameron's side after a worrying 0-3 start.
"Even when we were 0-3, deep down I knew we were playing some OK footy," Cameron said.
"But in six days we play (Western Bulldogs), probably the best side in the comp."