Halfback Hynes threw the last pass for the two tries that put Cronulla on top at the break on Friday night, then sent captain Cam McInnes over to make it a three-score game in the second half.
The Eels then scored twice in two minutes to make a game of things while the Sharks lost Jesse Colquhoun to the sin bin for a professional foul.
But Cronulla fullback Will Kennedy, in career-best form, sealed the result by putting winger Sam Stonestreet over for his second try in the final 10 minutes.
Hynes's superb performance came only five days after he and halves partner Braydon Trindall were questioned for failing to take control in an extra-time loss to Wests Tigers.
"We came down with a thud from a 90-minute game that you don't win. The boys just rocked up ready to go," said Sharks coach Craig Fitzgibbon.
"Give or take a couple of minutes where we had Jesse in the bin, we were playing well."
The Sharks' attack was more assured than in the Tigers clash, with Hynes first swinging left to put KL Iro in for a try on the centre's return from a hamstring injury.
Cronulla's next four-pointer came as Hynes's favourite collaborator Briton Nikora grabbed the halfback's pass and skipped behind Dylan Brown en route to the tryline.
"(Hynes) is in a really good place," said McInnes, the beneficiary of Hynes's third try assist.
"Regardless of what's said on the outside, he's doing so may good things for our team. He was outstanding tonight."
After a week of scrutiny on the NRL's use of the sin bin, referee Peter Gough banished only Colquhoun for an open-and-shut professional foul when the Sharks forward held Dylan Brown back in support.
"The sin bin is an obvious sin bin, from our point of view," said Fitzgibbon.
Wooden spoon favourites only a matter of weeks ago, the Eels continued encouraging signs since the return of star halfback Mitch Moses, particularly in the period when Colquhoun was off.
"Frustration (with the loss) but I can see where we're heading. That's the feeling," said Eels coach Jason Ryles.
"The players definitely get confidence when he (Moses) is getting ready in the sheds. There's no doubt about it.
"Everyone sees the talent that he's got but what I love about him is that he turns up every day and he competes and he drives standards and he wants to get better every day."
While the Eels had an extra man, winger Josh Addo-Carr sealed his double on a shift down the left before Moses snapped up J'Maine Hopgood's offload and connected with Brown on the next set.
Moses showed his renowned competitive streak earlier in the game, engaging in a verbal sparring match with Trindall when the Sharks five-eighth hit him late off the ball.
"It's just two halves competing," Moses said with a grin.
Dally M leader Kennedy had earlier set up Stonestreet's first try with a quick grubber kick and put paid to the Eels' comeback when he and Hynes linked up to send the rangy winger over again.
The Sharks lost Sifa Talakai to a game-ending head knock, with the forward set to miss next Sunday's clash against Manly.
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