It was the first time the club has won three straight games without their inspirational playmaker, and suggests their premiership chances aren't over yet despite losing both Thurston and co-captain Matt Scott to season-ending injuries.
The win came despite a second-half breakdown in discipline and ball-handling from the Cowboys, with their completion rate dropping from 85 per cent to 76 per cent by the end of the game.
They also appeared to have continued their unlucky run of injuries, with winger Antonio Winterstein sidelined with a calf injury while Scott Bolton and John Asiata both had scares but returned to the field.
An opening salvo penalties saw both teams given perfect attacking opportunities, with the Cowboys denied by a fast hand on Jake Granville's arm at dummy-half before Lachlan Coote defused Adam Reynold's grubber, only to be tackled high and earn a penalty.
It was the Rabbitohs who scored first, when an error followed by a penalty from the Cowboys gave Souths the attacking field position. Two right-foot steps from Adam Reynolds close to the line created some space on his inside and the halfback sent Cody Walker through to dive over between the posts.
The Cowboys immediately struck back, with Jason Taumalolo taking a short ball from Granville to crash over and post North Queensland's first points.
Despite several penalties going against them the Cowboys managed to take some form of control of the game, and they took the lead when a cut-out ball from Lachlan Coote found Kyle Feldt unmarked for his team's second try.
Granville notched up his second try assist in much the same way as his first, feeding a short ball to Coen Hess who crashed over to make three unanswered tries for the Cowboys leading into half-time.
It was end-to-end football for the first five minutes of the second half, but once again Reynolds' kicking game wasn't up to scratch, with his high kick being fielded by Feldt in-goal. On the ensuing set Cowboys pivot Te Maire Martin went within a metre of the line, and soon after Sam Burgess made his second error of the afternoon, knocking on as he worked it out of his own end.
Cowboys hooker Jake Granville didn't waste any time making use of the field position, catching Reynolds out of position to scoot through a gaping hole and claim a try to go with his two assists.
Souths seemed to spot a golden opportunity when Martin knocked-on in the face of the Rabbitohs defenders, but they spilled the ball a metre away from the Cowboys' line as their completion rate fell to 50 per cent.
It finally came together for the Rabbitohs after a strong set resulted in Braidon Burns crossing out wide when Cowboys' defensive line, absent an injured Winterstein, was caught out by a fast pass from Robert Jennings.
The errors for both sides began to pile on, with the Rabbitohs losing the ball through Robbie Farah before Scott Bolton did the same to bring the second-half errors to eight each.
The Cowboys eventually put consecutive sets together and Coote decided to get some finals practice in, taking the opportunity to slot a field goal and take the Cowboys' lead to 13 points.
Cowboys 23 (Jason Taumalolo, Kyle Feldt, Coen Hess, Jake Granville tries; Ethan Lowe 4 goals) def. Rabbitohs 10 (Cody Walker, Braidon Burns tries; Adam Reynolds 1 goal) at Barlow Park. Half-time: 16-6. Crowd 11,217
NRL.com unofficial votes: 3 points - Jake Granville; 2 points - Scott Bolton; 1 point - Kyle