Staring down the barrel of a fourth straight defeat to start the season, Souths overturned a slender halftime deficit and then held on for victory at Accor Stadium.
It came in another dramatic Good Friday clash, with the Bulldogs losing winger Josh Addo-Carr to a sickening 40th-minute concussion.
Charging down the left touchline, Addo-Carr's head was collected by Latrell Mitchell's leg and he will now miss next week's match against the Sydney Roosters.
Josh Addo-Carr receives attention after a heavy collision on the halftime siren. (Mark Evans/AAP PHOTOS)
Canterbury second-rower Jacob Preston was also struck down amid claims of a hip drop, but was able to stay on the field and recover.
The win was only Souths' fifth in 17 matches dating back to when they sat near the top of the ladder last June, and followed a month of scrutiny around Demetriou.
"I don't come to work every day worrying about whether I'm gonna have a job or not," Demetriou said.
"I come to work knowing that I've got a job to do to help these guys get prepared to play footy.
"I'm not going to put my head noise onto them. It's for me to deal with.
"I've got to concentrate on making sure they they know I believe how good they are. And I feel like we did that pretty well."
The Rabbitohs' win came largely thanks to their dangerous left edge bouncing into life.
Jack Wighton scored a double, while Alex Johnston and Mitchell were also influential.
After Tom Burgess scored the Rabbitohs' first, Mitchell put Johnston into space before Wighton scored later in the set.
Jack Wighton was a driving force in Souths' win, with two tries. (Mark Evans/AAP PHOTOS)
And after the Bulldogs took the lead 12-10, it was Wighton and Johnston who again combined after the break when they traded passes before the former crossed.
Souths also managed to resist several second-half attacking raids, only relenting late after two penalty goals gave them an eight-point buffer.
The only concern for the Rabbitohs was a hamstring injury for Johnston, with the winger unable to finish the game.
It was hardly a pretty victory from Souths, but it was desperately needed.
"We walked in Monday morning confident still, because we knew what we're capable of," captain Cameron Murray said.
"We didn't put too much pressure on ourselves. The pressure is from the outside."
Earlier, it had been Canterbury who looked the more dangerous with their own left edge threatening.
Burton scored their first when he hit a deep-running Viliame Kikau, who put Addo-Carr into space before Burton popped up on the inside to score.
The five-eighth also kicked a booming 40-20 in the lead-up to the Bulldogs' second, before Blake Taaffe stepped around Wighton and produced a perfect chip-kick for Connor Tracey.
Kurtis Morrin had a chance to put them 18-10 up before the break but dropped the ball as he charged over the line.
From there, Addo-Carr's absence and the Dogs' reshuffle stunted their attack, leaving both sides with one win from the opening four rounds.
"We're trying really hard. I can't fault their effort," Canterbury coach Cameron Ciraldo said.
"And that's a massive improvement on where we've been. But at some stage, we're going to need to execute better."
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