The Cowboys exploded out of the blocks and despite the home side threatening another remarkable comeback, they pulled away in the second half as the Sharks blew a series of chances.
The Cowboys launched an opening blitz with the help of some uncharacteristic blunders from Sharks fullback Michael Gordon, racing to a 10-0 lead before the Sharks had even touched the ball.
Tariq Sims was first to score at the end of the first set of the game when Gordon spilled a Robert Lui bomb into the Newcastle-bound forward's arms in front of the posts.
At the end of the next set Gordon made a mess of a tricky Rory Kostjasyn grubber and as he looked to regather, he batted the ball back infield which almost led immediately to a try but Kostjasyn was ruled to have touched the sideline just before he grounded the ball.
It mattered little as some Johnathan Thurston magic - wearing No.16 in honour of Alex McKinnon in Rise For Alex Round - from the ensuing set at the Cronulla line made the Sharks pay. After almost sending Sims over for a double Thurston dummied and went himself, his tough sideline conversion hitting the post for a 10-0 advantage after four minutes.
A scrappy and penalty-laden 15 minutes followed, with the Sharks unable to capitalise on plenty of good field position, and Ashton Sims and Lui each finding themselves on report for high shots on Sharks winger Jacob Gagan and Andrew Fifita, respectively.
The former hit caused Gagan to come off for a concussion assessment, with the versatile Luke Lewis shifting to centre and Jono Wright moving to wing.
The Cowboys were next to score, however, when they found the Sharks short on the right and a quality Michael Morgan cut-out pass put Antonio Winterstein over inside the left hand corner post, Thurston nailing the sideline chance from his preferred side for a 16-0 lead.
The Cowboys continued to dominate field position and but for a couple of great efforts from Fifita in fielding grubbers in his own in-goal that averted two goal-line dropouts it could have been worse.
The Sharks eventually clawed some momentum back and finally got on the scoreboard five minutes before the break when Wright did well to mark a Nu Brown cross-field bomb.
With half-time looming and a 10-point deficit appearing likely, the Sharks charged downfield with the help of a penalty and some quick hands to the right found makeshift centre Lewis, who stepped off his right foot past a couple of defenders to earn a much needed try.
Michael Gordon's conversion brought up 1,000 career points in the NRL – 202 of those for the Sharks – and despite a frantic late flurry where they seemed every chance of scoring a third try in five minutes the play broke down when a Jeff Robson pass after the siren headed into touch.
The second half started almost like the first in reverse, with the Cowboys fumbling their first kick reception but the Sharks were unable to make them pay.
The home side then had to absorb several repeat sets on their own line and in a credit to their defence, Thurston eventually opted to take twp points from a penalty and an 18-12 lead after 50 minutes.
A lost ball from acting Sharks skipper Wade Graham after the side had defused yet another Cowboys raid proved costly as Morgan first earned his side a repeat set with a clever grubber then cashed in by pushing through a tackle, showing remarkable strength to shrug through four defenders while keeping the ball off the ground to reach out and score.
With Gagan already gone for the game Cronulla then lost Siosaia Vave with shoulder and knee injuries with 20 still to play.
The home side's best chance at another miracle comeback came undone after Anthony Tupou found himself in space and one-on-one with Morgan, but looked to pass too late and lost it in the Ashton Sims tackle.
More dominant field position soon told on the luckless Sharks when Cowboys lock Glenn Hall ran onto a short ball at the line for a 30-12 lead, before a controversial try to Thurston then put the match out of Cronulla's reach.
After grubbering to Gordon, he stripped the ball from the Sharks fullback after the previous defender had bounced off. He raced away to score and despite the on-field officials sending it up as a 'no try', the video referee deemed the tackle a one-on-one strip because only one player was in contact with Gordon at any time.
A late consolation try to Gordon narrowed the gap to 36-18 but it was the Cowboys who were left celebrating their first away win since their Round 25 trip to the venue in September last year.
North Queensland Cowboys 36 (Johnathan Thurston 2, Tariq Sims, Antonio Winterstein, Glenn Hall, Michael Morgan tries; Thurston 6 goals) def. Cronulla-Sutherland Sharks 18 (Jonathan Wright, Luke Lewis, Michael Gordon tries; Gordon 3 goals). Half-time: 16-12 Cowboys. Crowd 9,366.