Red-hot centre pairing Jake Averillo and Herbie Farnworth helped the Dolphins flaunt the attacking vigour that made them the league's most prolific scoring team last year.
But holding back-to-back preliminary finalists Cronulla to 10 points, after they scored 50 in their last home game, was even more encouraging as the Dolphins lay the groundwork for their first finals berth.
"(The win) should give us some real belief and gives us an idea of different ways we can win games nowadays. That's really important," said coach Woolf.
"It's a great win for us. A couple of years ago we couldn't win in Sydney.
"This was our first chance down here this year at a very, very tough place to come and win, and we've come up with a great performance."
With the scores level in Saturday's first half, Farnworth crabbed to the right in the red zone to unsettle the Sharks defence and picked out Isaiya Katoa.
The halfback's cut-out pass hit Jamayne Isaako, who crossed on the right edge to silence the crowd.
In the final two minutes of the first half, Farnworth found himself on the outside of his opposite man Jesse Ramien and then broke free from Sione Katoa.
Farnworth then offloaded for a flying Hamiso Tabuai-Fidow to give the visitors a 16-4 halftime lead.
Asked whether English international Farnworth was the NRL's best centre, Woolf quipped: "I think he is, and he thinks he is as well."
For his part, Averillo had the Dolphins' first try on a shift to the right before gathering a loose ball to stretch the lead to 16 points in the final 10 minutes.
The Dolphins' victory ends a run of eight consecutive wins for Cronulla at Shark Park.
Braydon Trindall's 100-game milestone and last week's big loss to Penrith should have given Cronulla plenty of motivation.
But the Sharks' attack was sluggish from the jump, and coach Craig Fitzgibbon was disappointed with his side leaking three tries in the last six minutes.
"At the moment, at the back end of a game like that where we concede cheap ones and easy ones, they hurt," Fitzgibbon said.
"Maybe we need to hurt a bit until we do something about it."
Selwyn Cobbo and Connelly Lemuelu crossed after the result was beyond doubt with punters streaming out of the stands.
Blayke Brailey's league-leading streak of 133 consecutive games could be under threat after he went on report.
The Sharks captain was ruled to have tripped Tabuai-Fidow on a kick chase in the second half, allowing the Dolphins to kick for an eight-point lead from the penalty.
"The club will look at it, hopefully I'll be playing next week," Brailey said.
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