The Roosters were on the back foot from the opening minute when they conceded a ruck penalty before Cowboys centre Winterstein scored in the eighth minute, strolling through some feeble defence to score under the posts.
Winterstein had a double three minutes later when he scored on the left edge and Johnathan Thurston added the extras to make it 12-0.
The Roosters continued to backpedal and struggle in the conditions before winger Ashley Graham finished off a nice backline move to score in the right corner to make it 16-0.
Three minutes later, the Cowboys produced another sweeping backline play with Kalifa Faifai Loa diving over in the corner which Thurston converted to make it 22-0.
A drinks break stemmed the flow of points for the Roosters but, soon after the resumption, Thurston produced a brilliant banana kick that fullback Bowen pounced on to score next to the posts.
The Roosters sat in a coolroom at halftime and it looked to have brought them to life with centre Shaun Kenny-Dowall spectacularly climbing above the pack to snare a Mitchell Pearce cross-field kick to score six minutes after the break.
Braith Anasta put a towering cross-field kick up with centre Joseph Leilua bringing it down close to the posts to score a converted try and there was a faint hope of a comeback at 28-12.
But the Cowboys killed off any hope the Roosters had when powerful interchange forward Taumalolo burst through from close range to score on the back of a penalty to score under the posts to make it 34-12.
The Cowboys dominated the final 12 minutes with soft tries to Ray Thompson, Taumalolo and Bowen.
North Queensland front-rower Ashton Sims was placed on report for a high shot on Roosters back-rower Jack Bosden in the second half.
NORTH QUEENSLAND 50 (M Bowen 2 J Taumalolo 2 A Winterstein 2 K Fai Fai Loa A Graham R Thompson tries J Thurston 6 M Bowen goals) bt SYDNEY ROOSTERS 12 (S Kenny-Dowall J Leilua tries B Anasta 2 goals) at TIO Stadium. Referee: Gavin Morris, Ashley Klein. Crowd: 10,008.
- AAP
