The reigning champions fell behind early on as Dragons winger Fouad Yaha ran in the first try of the season.
But, the Saints remained calm and picked apart their opponents, with England winger Tom Makinson scoring two tries, while debutants Joey Lussic and Konrad Hurrell added to the lead.
St Helens coach Kristian Woolf is hunting a third successive Grand Slam title this year, but was keen to keep his side's feet on the ground after their first win.
"It's round one, so you can't get too excited," Woolf said. "There is a lot of footy to be played, but it gives us a lot of confidence.
"I said before the game we were in a good position to attack the season and I think we showed that tonight. It's a great little block for us to build off and we're only going to get better from here.
"It was a good tough physical game of footy and, when the game got flowing, there was some real positives and I thought our blokes put on some outstanding tries.
"But there were periods of real stop-start. We want people to come and watch our game and we want to entertain and we've got to do something about this slowing down and stopping and holding down in the ruck, it just made it ugly at times."
Woolf reserved extra praise for former Leeds Rhino centre Hurrell, who shone on his debut, first setting up James Roby's try before scoring one of his own following an interception.
"I thought Konny was exceptional," Woolf said. "I remember when we signed him, I said, 'If we can get him fit and get him happy, we can get a real performance out of him'.
"He's got to back that up next week, but he was great out of yardage and defended really well. A couple of tries came off the back of his little offloads and that bit of X factor he's got about his game."
The Saints will undoubtedly be pleased in the way they dispatched their opponents, but they'll still be disappointed at a number of wayward kicking opportunities.
Lewis Dodd, usually reliable with his boot, missed three of his five attempts at goal, while Makinson also tried and failed.
Luckily for the Saints, it didn't affect Thursday's result, and Woolf was confident that it was simply a one-off.
"It was a tough night for that," Woolf said. "It was slippery and windy and the majority of our tries were scored out wide.
"The goal-kicking was not as good as you'd like it to be, but it will get better, there's no dramas there at all."
St Helens are next in action on February 19, when they travel to Hull KC. As for the Dragons, they'll look to bounce back against Wakefield on the same day.