Tom Symonds crashed over off a Daly Cherry-Evans pass in the 54th minute before Jorge Taufua forced his way over out wide off a Stewart pass six minutes later.
Cherry-Evans sealed the win with a 76th-minute field goal, before Jason Nightingale scored a late consolation try in acrobatic style for the home side.
After co-competition leaders Penrith and Canterbury suffered losses on the weekend, Manly sit alone atop the NRL ladder on 28 points.
After a disappointing effort following four wins in their last five starts, the Dragons sit a win outside the eight on 20 points, with Josh Dugan their best.
Manly had won just one of their previous six encounters at the venue and Geoff Toovey was glad to put a dent in that record.
"We have always had trouble winning here, it was a tough win from our blokes," he said.
"I thought we defended really well."
Matai left the field for Manly with a knee injury in the first half but returned after the break.
Toovey said Matai had a bad cork but would be fit for Sunday's away match against the Warriors.
However, interchange forward Dunamis Lui is in doubt with a knee problem.
Dragons coach Paul McGregor bemoaned his team's ability to put together an 80-minute performance and fix their right-side defence.
"Our first half was really good," he said.
"I thought we were good for long periods - just not for 80 minutes."
McGregor said his team needed to win four of their last seven games to make the finals.
- AAP
