An eventful start was capped when Mitch Rein scooted over from short range, the Dragons rewarded for an opening in which they showed surprising endeavour with the ball.
The home side continued to chance their arm but the Sharks were gaining in confidence from their ability to repel, Graham's powerful first seeing him bust through a feeble Nathan Fien attempted tackle.
The Sharks were coming hard as halftime approached and as Todd Carney chased a lead, he threw a poor pass behind his runners, Brett Morris scooping up the crumbs and racing 75 metres to score as the hooter sounded.
Cronulla applied the squeeze to open the second stanza, Jeff Robson securing a repeat set with a neat grubber before laying on a delayed ball for Graham to spear over to leave the Sharks trailing 12-10.
Another Robson repeat set and Graham attempted to turn provider only for his ball to a runaway Anthony Tupou to be called forward, Cronulla receiving no such favour from the referees as Merrin clinched the win.
-AAP