Down by two points with 90 seconds remaining and seemingly out of ideas in attack on tackle five, the Green Machine spread the ball from sideline to sideline before it eventually ended up in the hands of Xavier Savage.
An unfamiliar kicker, Savage managed to poke a grubber through to fullback Kaeo Weekes.
Weekes flicked it on to Simi Sasagi who delivered a final inside ball for Sebastian Kris to score the try that sent the 10,000-strong Canberra faithful and coach Ricky Stuart into raptures on Thursday night.
"You've seen what this club is about in that last minute-and-a-half. You've seen what this club is built on," said an elated Stuart, who had been last seen holding two Raiders staff members in a celebratory headlock following the match-winner.
Their win comes despite being temporarily reduced to 12 men after the NRL's latest high-tackle crackdown claimed its first victim.
Canberra second-rower Hudson Young was sent to the sin bin for a relatively innocuous shot on Cronulla captain Cameron McInnes in the 58th minute.
Coaches had been put on notice by the league ahead of round six that direct forceful contact to the head would result in 10 minutes on the sidelines.
But if Young's hit was direct and forceful, it was hardly more so than a shot from Cronulla forward Billy Burns on Matt Timoko in the first half that referee Todd Smith deemed worthy only of a penalty.
The dramatic finish was the only moment of note in an otherwise dour second half.
The five-day turnaround took its toll on both teams in the end, Sharks coach Craig Fitzgibbon suggested.
"I think we were both out of gas at the end there," he said.
"We just couldn't find a way, and they found it in that last play.
"I thought it was a pretty even match in the end but our execution's just a little off at the moment."
It was a stark contrast to a frenetic first half, in which Canberra and Cronulla went try for try, scoring three apiece to enter the interval level locked at 18-all.
First Matty Nicholson stormed over for the home side, before Mawene Hiroti, deputising in the centres for the injured Kayal Iro, split the gap between Timoko and Savage three minutes later.
Then Young got on the end of a Tom Starling grubber kick, only for his try to be cancelled out by Briton Nikora's first of the match following some limp defending by Kris and Ethan Strange.
A second try for Young was followed by another to his opposite number.
Nikora, latching onto the ball after a breakdown in the attack on the last tackle, attempted to grubber past Canberra No.13 Corey Horsburgh.
The ball ricocheted off Horsburgh's knees and back into the path of Nikora, who instinctively stuck out a toe, kicked it a third time, and dotted down in the in-goal.
The win lifts Canberra into the top eight as they prepare for a tricky trip to Darwin to face bottom-dwellers Parramatta.
After two losses on the trot, and following another disappointing showing from talisman Nicho Hynes, Cronulla face a difficult away trip to a high-flying Manly side.
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