A crowd of 9271 - including one group who watched the game from a tent on the hill - braved the miserable conditions at Toyota Stadium to watch a contest between two sides adept at wet weather football.
And despite being without skipper Paul Gallen, as well as Andrew Fifita and Wade Graham, it was the Sharks who raced home on the back of Robson's brace.
The former Parramatta and Manly half slid over for the first of his two tries when backing up a Jeremy Smith break with 11 minutes to play, and barged over for the match-winner just three minutes later.
His second try came on the back of an outstanding 40-20 kick from five-eighth Todd Carney, and was followed by Carney's match-winning conversion.
The Sharks needed to defend until the final whistle, with Warrior Shaun Johnson going perilously close to sneaking over with two minutes left as Cronulla held firm.
Earlier, Konrad Hurrell had extended the Warriors' 13-8 halftime advantage when he barged past two Cronulla defenders to score out wide in the 51st minute, while a penalty goal to James Maloney five minutes later pushed the lead out to 11.
The Warriors enjoyed the better of the first half, with a Johnson try six minutes from halftime capped off by a James Maloney field goal.
While Johnson capitalised on a cross-field kick from Maloney to dot down, it was the five-minute defensive effort they weathered from the 22nd minute, in which Carney earned three repeat sets for the Sharks with perfect wet weather tactics.
The pressure was only relieved when Maloney's third drop-out was allowed to bounce into touch by Colin Best, a moment which changed the momentum of the first half.
The Sharks had opened the scoring in the fifth minute when Warriors rookie Omar Slaimankhel, a late replacement for injured winger Manu Vatuvei (knee), made the worst possible start to his first-grade career.
The 20-year-old dropped the ball on a kick-return in a solid tackle by Isaac Gordon, with Ben Pomeroy crashing through three defenders to score one tackle later.
It didn't take long for the Warriors to hit back, Johnson putting in a delightful grubber which fullback Kevin Locke brilliantly grounded.
The visitors suffered a blow 15 minutes after halftime when Micheal Luck, playing his first game for 2012 having recovered from a shoulder injury, limped off with a leg complaint.
Pomeroy was placed on report late in the first half for collecting Ben Henry in the head with his elbow while making a tackle.
Asked if the Sharks had stolen the win, coach Shane Flanagan said: "To a certain degree.
"I thought if we hung in there, we'd eventually get some points. But it was probably one you could put in that category."
Carney revealed he'd been in doubt right up until game day with a cork picked up in the Blues' 16-12 Origin win.
"I was a little bit rattled (on Friday). I didn't train with the team," he said.
"But this morning was surprising - I felt pretty good.
"I wanted to turn up and play the best I could and work on from Wednesday, and continue my form for the Sharks.
"Obviously it's a completely different role when I come back here and I just wanted to come out and play the best that I could for the boys."
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