The Cowboys had an 18-6 lead after the break when Jake Granville burrowed over from dummy half.
Mark Ioane - who only arrived at the Dragons this week after making a mid-season switch from Gold Coast - set up a grandstand finish when he came up with a spectacular four-pointer in the corner, however the Cowboys held on.
Earlier the visitors took a 12-6 lead into the break thanks to centre Linnett's first-half double.
North Queensland jumped to an early break in the third minute when Linnett, who grew up in nearby Port Kembla, mopped up when Gavin Cooper had the ball stripped close to the line.
When Benji Marshall drifted across field and found a hard-running Euan Aitken, the Dragons levelled things up before Linnett pounced on a Robert Lui grubber to give his side the advantage at halftime.
Dragons winger Kiti Glymin's debut was soured when he was taken off with a hamstring injury, while North Queensland's Antonio Winterstein sat out the second half - also with a hamstring problem.
After fading badly against Cronulla last week, coach Paul Green said winning without Thurston and their other Origin stars was a valuable lesson heading into the finals.
"It's huge for the team's confidence," he said.
"They understand now that it doesn't matter who puts the jersey on. They know they've got a job to do and there's an expectation that they do it regardless of who it is.
"It just adds to that confidence."
Dragons coach Paul McGregor said Glymin was in a bad way and expected to spend an extended stint on the sidelines.
After being entrenched in the top four for most of the year, the loss puts the Dragons on the edge of the top eight with a logjam of teams on 20 points.
However, McGregor said he wasn't beginning to doubt his team, pointing out their past three losses had been by six points or less, and there had been more than a few disruptions during the week.
"There's no panic stations but you'd like to start to win games, that's for sure. It's really important," he said.
"The guys worked hard to put themselves in a good position on the ladder and when you lose consecutive games you drop down pretty quickly.
"We're not happy with that. The situation for us is the last three games we were in it right to the end but we couldn't manage a win and tonight was no different."
- AAP
