The Giants held a six-point lead at halftime, but their tsunami style swamped Brisbane in the third quarter, outscoring the Lions 14.2 to 0.3 on their way to a 26.10 (166) to 13.10 (88) win at Engie Stadium on Sunday.
The onslaught eclipsed the 13.4 Essendon kicked in the third term against Footscray in 1982 as the highest-scoring third term in VFL/AFL history.
GWS also registered their biggest ever score, going past the 25.12 (162) they posted against Essendon in 2023.
Greene, whose future has been the subject of much talk in recent weeks, kicked five goals, four of them in the third quarter.
With his third major, Greene passed Jeremy Cameron's GWS individual record of 427 goals, with coach Adam Kingsley revealing the Giants leader had been playing under duress.
"He's been playing with a broken foot for the last five weeks,'' Kingsley said.
"He still shows up and performs, he won't let me rest him - he's just such high quality.'
"I was pleased with the whole game, not.just the third quarter, but everything we touched turned to gold."
To back up Greene's superb effort, Jake Stringer pitched in with five goals of his own, and Max Gruzewski and Aaron Cadman scored three each.
"Its probably the best footy we've played in 12 months to be honest," GWS defender Lachie Ash told AAP.
After being totally blown away in the third term, Brisbane kicked the first four goals of the final quarter, but GWS booted the next three.
Making the Giants' feat even more remarkable was the fact that their injury woes continued to mount.
They suffered a blow before the match when veteran Lachie Whitfield was ruled out with hamstring awareness and was replaced by Harry Oliver.
The Giants then lost key defender Jack Buckley to a hamstring issue in the first quarter.
Brisbane coach Chris Fagan never saw the third-quarter blitz coming.
"We can choose whether we get better from it or continue to go backwards, because at the moment we're nowhere near a premiership fancy at at all," he said.
'We're just battling to find.our form at the moment."
Lachie Neale gathered a team-high 32 touches for Brisbane, and Cam Rayner and Kai Lohmann each kicked three goals.
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