In wind and rain, the Tigers became the first team to successfully overturn a Dragons halftime lead this season, finishing strongly with three second-half tries after trailing 8-4 at the break.
The pivotal moment in the game came in the 51st minute when Moltzen claimed his second try, pouncing on a Robbie Farah grubber to give the home side an eight-point lead at Allianz Stadium.
The decision was sent to video referee Bernard Sutton who watched more than a dozen replays involving Dragon Ben Creagh potentially getting his hand to the ball first. He eventually awarded a benefit-of-the-doubt try.
Moltzen opened the Tigers account just two minutes before the break, putting in a top shelf performance against the club he refused to join in the off-season - and erasing memories of a horror match against the Dragons in round three.
The classy fullback sealed the win and claimed his hat-trick eight minutes from time when he accepted a brilliant inside pass from Benji Marshall to cross near the posts.
Moltzen's tries were split by one to makeshift Tigers five-eighth Liam Fulton after the visitors bolted to an eight-point lead through unconverted tries to winger Brett Morris, who also scored a double, and hooker Mitch Rein after just 14 minutes.
The visitors enjoyed the best of the opening 40 minutes with halves Nathan Fien and Ben Hornby playing to the conditions better and providing a superior kicking game to Marshall.
But Farah took control after the break, kicking with purpose and forcing a number of repeat sets in good position.
The loss leaves the Dragons four points behind eighth spot with a poor for and against and just three matches remaining, but moves the Tigers to 26 points and potentially one win from securing a finals berth.
Fien was sent to hospital after suffering an arm injury in the 50th minute, with Jamie Soward finishing the game in the halves after starting on the bench.