"During that period the boys handled it really well, we had field position well and finished off strong," Dragons coach Paul McGregor said.
"It's great going forward. You don't come here to win pretty, you come here to scrap to win. And we scrapped well tonight."
Ben Hunt and Gareth Widdop again showed the potential of their combination, as the Red V made use of a blustery wind at their backs in the second half.
They kicked for both of the Dragons' initial two tries of the comeback, Widdop's first highlighted by a miraculous leaping Nene Macdonald effort to get the ball down before his feet went out.
After Hunt fortuitously put Tyson Frizell in via a miskick following the halftime break, he and Widdop combined to put Euan Aitken outside his opposite centre to score.
Aitken also played a key role in the win, having moments earlier forced the ball loose from Josh Dugan as the former Dragon crossed the line in his first game at fullback for the Sharks.
But the Sharks were their own worst enemy, completing at just 40 per cent in the second half after making just one error in the first.
"We're terribly disappointed in our second half," coach Shane Flanagan said.
"You just can't do it. Some of those errors we made today in that second half were just fundamental.
"Coming off our line we dropped the ball on tackle one or tackle two too many times. I lost count."
It came after a first half where five-eighth recruit Matt Moylan's increased involvement had him force two drop-outs and set up a try for Sosaia Feki with a bullet cut-out pass.
Meanwhile, Valentine Holmes had an unhappy night back on the right wing, running just four times for 34 metres.
He was jumped over by Macdonald for the Dragons' first try, threw an intercept as the Sharks mounted pressure late in the opening half and then made another error early in the second.
- AAP