Souths (3-4 record) became yet more roadkill in Townsville. North Queensland (5-2) have now won 13 of their past 15 home games and outscored visiting sides 179-32 in the past five games in the north.
Coincidentally, South Sydney were the last team to beat North Queensland in Townsville, in round 23 in 2015.
It marked the first time the Cowboys had won first four home matches of a season since 2005.
Thurston sparked a backline boosted by the return of centre Kane Linnett from a shoulder injury.
Thurston helped North Queensland lead 18-6 at halftime when he scored off his own grubber in the 15th minute and kicked three conversions.
He brought up his milestone with the third conversion thanks to a slice of luck: the kick ricocheted off the post but still fell over the crossbar to register point No.1001.
The Cowboys concede their first points in three home games when Reynolds and Luke Keary combined to set up barnstorming backrower Chris Grevsmuhl, locking up the scores at 6-6 in the ninth minute.
Then it was all one-way traffic.
Asked if his side could improve, North Queensland coach Paul Green said ominously: "Yep.
"How long is a piece of string. It's a continual journey.
"You are always looking at how you do things better.
"The moment you stop and pat yourselves on the back, teams go past you."
Scott was not concerned with being placed on report.
"I don't think I got him high," he said. But there were plenty of worries for Souths coach Michael Maguire after their fourth loss in five games.
"We are dancing around it. The way this side is playing is not like South Sydney," former NRL hard man Gorden Tallis told Fox Sports TV.
"Are we showing too much respect for what they have achieved in the past?
"With that roster they should be performing better."
In another concern for Maguire, Hymel Hunt was placed on report for a high shot on Cowboys backrower Gavin Cooper early in the second half.
-AAP
