Down by 35 points before the main break at Engie Stadium, the Giants needed the first goal when play resumed to keep their bid for a top-four finish alive.
Adam Kingsley's side got that when young gun Finn Callaghan answered the call with a dash down the corridor, setting up a 15.12 (102) to 8.10 (58) win on Friday night.
So dominant were GWS after early strife that they kicked eight straight goals - nine in total - in the third quarter for a 23-point lead at the final change.
The home side, powered by a halftime spray described by Callaghan as "the biggest he's ever given us", had kicked just three majors in the opening half.
Kingsley was less illustrative around his halftime message.
"Oh, just reminders around the way that we want to play and asking certain players to lift their output, really," Kingsley said.
"I love the way that the guys responded."
Snaring their first win in six derbies, the Giants have effectively ended their cross-town rivals' campaign to muscle into finals contention.
The in-form outfit move to fifth (13-6) with their sixth consecutive win, while Sydney languish in 10th (9-10) ahead of the weekend's clashes.
A serious head knock to Hayden McLean further soured the loss, the Swans forward stretchered off in the opening minute.
Sydney then lost defender Joel Hamling (hamstring) in the third quarter, while Giants veteran Josh Kelly's night ended prematurely with a calf complaint.
"It doesn't look good to start with," Swans coach Dean Cox said on Hamling's hamstring injury.
Callaghan earned his first Brett Kirk medal for his best afield performance, as captain Toby Greene proved their firestarter in a fierce battle with Swans livewire Tom Papley.
Greene had issued an ominous warning at halftime after Papley celebrated his first major on return from a hamstring injury by making a beeline for the Giants forward.
"He's (Papley) looking overweight," Greene told Fox Footy at halftime.
"Let's see how he goes in the second half."
Greene also had a pre-first-bounce tussle with Swans defender Dane Rampe before giving away a free kick for an arm to Isaac Heeney's head.
Aaron Cadman and Jake Stringer slotted three majors each, as defenders Harry Himmelberg and Lachie Ash got in on the goalscoring action with one apiece.
Errol Gulden led the Swans with 32 disposals, while Will Hayward was commanding in attack with three-straight majors in the opening half.
Sydney started the better side after finding composure following McLean's injury.
He clashed heads with Giants defender Jack Buckley in a marking contest.
Buckley had been pushed into McLean when Giants teammate Sam Taylor entered the contest and attempted to spoil the mark while wrestling with Swans player Jack Buller.
Play was delayed for six minutes as a conscious McLean left the field on a medicab, with Aaron Francis coming into the game in his place.
Sydney then kicked six straight goals to take a 28-point lead at halftime, before Greene issued his Orange Tsunami warning.
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