Broncos fullback Corey Norman then spilt a Carney bomb for Sosaia Feki to capitalise before Carney's crucial field goal.
Late tries to teenager Corey Oates and Jordan Kahu had the home fans on their feet but it was too little, too late for the struggling Broncos.
The Sharks had earlier lost stand-in skipper Wade Graham to a first-half shoulder injury while Mark Taufua was placed on report for a shoulder charge on Broncos halfback Peter Wallace.
Saying it had taken him longer to reach the 150-game mark than it should have because of his "holidays" following off-field incidents, Carney was pleased with his efforts.
He said he hoped the performance would kick him into gear as the Sharks prepare for a run at finals football.
"Last year, heading into finals time I had a few injuries and my form started dropping off," he said.
"Hopefully this is the game I needed to spark the final run home for the year."
Broncos coach Griffin, whose team is struggling to get into the eight after three straight losses, was proud of his team's efforts but acknowledged Carney had been the difference.
"It was a tough old game," Griffin said.
"Both teams gave everything and it just opened up right near the end there.
"We just gave them too much start though."
- AAP
