The Sharks were touted to make a late top-four surge with a bye in hand and up against only one of the top-eight teams in the final five rounds of the regular season.
Now, they will need to rely on Penrith to lose twice and the New Zealand Warriors to also drop points if they are to book a qualifying final spot.
Coach Craig Fitzgibbon admitted Cronulla missed a chance to shake up the top four, as the Dragons scored their first win over the Sharks in five years.
"We had an opportunity today and we didn't take it," Fitzgibbon said.
"I thought the game had no rhythm to it at all ... it was a poor discipline performance from us.
"We opened the door and showed we were susceptible, and they took it."
Debutant Hayden Buchanan and Clint Gutherson starred, scoring and setting up each other's tries to inspire a ferocious second-half Dragons performance at Jubilee Oval on Saturday.
But the win was bittersweet as big man Moses Suli limped off the field and had his right knee iced after coming off second best in a tackle.
It added to a injury-riddled week for the Red V, who lost Sione Finau and Michael Molo midweek.
"A lot of stuff has happened behind the scenes this week, injuries and so on, and a boy making their debut, so outstanding club effort," coach Shane Flanagan said.
St George's season still has a very faint pulse as they need to win every match and score a significant amount of points to overhaul their negative for-and-against.
Despite the win, Flanagan was unhappy with the officiating.
Teig Wilton was awarded a penalty try in the first half by the bunker after Tyrell Sloan tackled him midair.
Video referee Chris Butler said the Dragons winger had his fingers on the ball before Wilton stripped it and tackled him.
"Wow," Flanagan said.
"I'll have a busy day on Monday because it's just making it so hard for us.
"I'm really disappointed with a lot of decisions tonight."
Both teams started with energy in their legs, but it was the Dragons who drew first blood when Damien Cook punted the ball, finding a diving Emre Guler.
Cronulla upped their intensity, and tryscorers Braden Hamlin-Uele and Wilton benefited.
St George completed set-after-set and used their speed to pressure Cronulla, scoring three unanswered tries.
The Sharks had one more roll of the dice with minutes to go, but threw a forward pass, seeing out the eight-point victory margin.
Will Kennedy (211 metres, five tackle busts) and Siosifa Talakai (171 metres) were big contributors for Cronulla.
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