Thurston made amends for an ordinary first half by opening the scoring in the second half.
The Raiders seemingly then switched off after a penalty goal extended their lead to 20-6, Cowboys playmaker Robert Lui making them pay with another converted try.
But twinkle toes Raiders fullback Anthony Milford was finally rewarded for a brilliant run-on debut with a try off the back of a scrum in the 75th minute, putting the fast-finishing Cowboys to the sword.
Newcastle have moved into the top eight with a gutsy 18-12 victory over Canterbury in Mackay.
The Bulldogs took an early second-half lead in Ben Barba's North Queensland home town when Josh Morris scored after a strong run.
But tries to veteran hooker Danny Buderus in the 59th minute and Chris Houston 10 minutes later sealed the Knights' second win in a row - and lifted Wayne Bennett-coached Newcastle over the Bulldogs on the ladder - although the Dogs kept pressing until the end.
The teams were locked 8-all at halftime after a half where the Knights dominated territory but couldn't pull clear of the Bulldogs.
Houston and in-form wing James McManus scored the first-half tries for Newcastle while Josh Reynolds and Krisnan Inu crossed for Canterbury.
Home town favourite Barba, who went close to a try twice in the Dogs' opening set, had the fans on their feet when he stepped his way clear late in the half.
But a brilliant effort by Knights halfback Tyrone Roberts denied the Bulldogs fullback on the goal-line.
Raiders 26
Cowboys 18
Knights 18
Bulldogs 12
- AAP