Down 12-0 with an hour of the game gone, the Sharks scored two tries via Luke Covell and Brett Kimmorley before the veteran halfback potted over the one-pointer from 25 metres out to all-but confirm a top four berth.
The third straight loss left the Dragons in the logjam of teams near the bottom of the top eight, leaving what looked a probable finals spot a few weeks ago now in jeopardy.
Up 6-0 at halftime thanks to a mixture of good fortune and relentless goal-line defence, the Dragons doubled their advantage on 50 minutes when Josh Morris stood up Ben Pomeroy to join brother Brett in the tryscoring column.
Cronulla finally found some joy, with a Jamie Soward kick out on the full inside his own half leading to a miracle around the back flick pass from Brett Seymour which saw Luke Covell cross, the winger letting himself down with a simple conversion crashing into the upright.
Covell eventually got his two points when the Sharks were handed a soft penalty for a late hit on Brett Kimmorley as he got a kick away, while the Dragons were further stretched when Justin Poore was taken from the field on the back of the medicab with a knee injury.
Kimmorley ensured a tight finish when his ricocheted grubber led to a try beside the posts, and after missing with his first field goal attempt, he made sure of the win with his second.
The game was only five minutes old when Justin Poore let fly with a double face slap on opposite Ben Ross, but it was the Sharks looking dangerous with the ball.
They should have opened the scoring after 11 minutes when Ben Pomeroy attempted to bulldoze his way over Soward, who did brilliantly to hold up his much bigger opponent as he stood on his own line.
It was part of a sustained period of dominance for the home side, but their over-reliance on the poorly executed high kicks for the wings saw them continually come up empty handed.
The Dragons’ first real opportunity came on the back of a brilliant Soward 40-20, a set play at the scrum seeing Soward chip ahead for a flying Brett Morris to acrobatically touch down just inside the dead ball line.
The try came at a cost with Morris leaving the field with a shoulder injury soon after, the Dragons forced into a major re-shuffle with halfback Ben Hornby ending up at fullback.
Cronulla continued to get close, but not close enough, skipper Paul Gallen pushed into the corner post two minutes out from the break to cap a half of near misses.