The Giants appeared set for a thumping when Michael Voss's Blues, on a five-game winning streak, enjoyed a scintillating eight-goal first quarter at Engie Stadium.
But GWS booted seven second-quarter goals to revive the contest, then another seven in the third term to blow the game open - including a run of nine unanswered goals across either side of half-time.
The Giants had to withstand a late Carlton surge but held on for a 18.8 (116) to 16.8 (104) win.
Jesse Hogan booted five goals for the Giants, while Carlton's Charlie Curnow (one goal) was blanketed by Jack Buckley.
But it was in the midfield where the Giants turned the game around.
Giants ruckman Kieren Briggs (40 hitouts, 22 touches) monstered Tom De Koning, while Tom Green (33 disposals), Stephen Coniglio, Finn Callaghan, Lachie Whitfield, Toby Bedford and Callan Ward also stood tall.
"For the first quarter, we were nowhere near it. And after quarter-time, I thought we were pretty good," Kingsley said.
"Maybe the last 10 minutes of the game they got that control back and were able to put some score on the board and really make the game pretty tight in the end.
"But I was really pleased our guys responded.
"It's not often you're 33 points down at quarter-time, and you can respond like the way our guys did.
"So that'll give us an enormous amount of confidence. We know we've got it in us, but you've then got to do it, and we were able to do it tonight."
The victory lifts GWS (9-7, 36 points) to seventh while second-placed Carlton (11-5, 44 points) keep their noses in front of the chasing pack.
Carlton skipper Patrick Cripps (33 disposals and two goals) worked desperately, while Harry McKay booted five goals.
Key defender Jacob Weitering battled through the game after suffering a corked right thigh late in the first term.
McKay booted three goals inside the opening 10 minutes while former Giant Zac Williams chipped in with three of his own.
Trailing by 33 points at quarter-time, the Giants responded with the first four goals of the second quarter and cut the half-time deficit to two.
Hogan put the Giants in front for the first time a minute after the break, and kicked his fifth just before three-quarter-time to deliver a 36-point lead at the final change.
Carlton kicked a late flurry of goals to make the Giants nervous, but Adam Kingsley's charges held on.
"It was a game of momentum wasn't it?" Voss said.
"I thought how well we played in the first, you could equally say the opposite for the next two quarters.
"We were completely dominated in the second and third quarter.
"I'm really pleased that despite the day not being ours, we were able to play it out right 'til the end."
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