Bound for St George Illawarra next year, the talented custodian set up three crucial first-half tries to put the hosts on the front foot in Townsville.
The Cowboys pack - superbly led by Jason Taumalolo, Matt Lodge and Thomas Mikaele up front - were key to the victory.
"We played direct, we played upstream and we ran hard," Cowboys coach Todd Payten said.
"When we kick to corners and stay patient the opposition break more often than not."
The Rabbitohs were playing for the first time since the sad news that forward Jai Arrow was battling motor neurone disease (MND) became public knowledge.
Both sides were without key players due to State of Origin and injury, but still turned on a highly competitive match.
Drinkwater set up the first try with a deceptively delayed long pass for winger Zac Laybutt to open the scoring.
Debutant Rabbitohs winger Talanoa Penitani, who scored a double and looked a star of the future, had a stellar start to his NRL career to finish a try courtesy of a perfect looping pass by reborn fullback Matt Dufty.
Penitani impressed coach Wayne Bennett but is set for a stint on the sidelines after an incident when he was on his way towards a hat-trick at the end of the match.
"I really liked him until he pulled a hamstring halfway down the field when he should have scored a try. He was going really good," Bennett said.
Veteran playmaker Cody Walker was busy and kept the Rabbitohs in the game.
Cowboys hooker Reed Mahoney has proven to be an outstanding signing. His 40/20 and support play to score a try from a Drinkwater pass after a Jake Clifford intercept stamped his class and enthusiasm.
Another explosive Drinkwater dart and offload sent elusive centre Tom Chester in for an 18-6 lead at the break.
The Cowboys had chances to put the game away early in the second half but failed to land the killer blow.
Rabbitohs half Ashton Ward showed great desperation to latch on to a charged down kick by Drinkwater. He then threw a cut-out pass to put Penitani in for his second.
Chester made several try saving tackles to deny Rabbitohs whiz Alex Johnston to show he is more than just an electric attacker.
Johnston did cross the stripe to become the first player since Phil Blake in 1983 to score a try in 10 successive games.
Cowboys second-rower Heilum Luki, who had a try disallowed in the first half, capped a superb game with the match-sealing four-pointer to further enhance his Queensland credentials for State of Origin.
Bennett said his team's performance was "very mixed".
"The effort was great but execution wasn't," he said.
The Rabbitohs also lost forward Adam Elliott to what Bennett said was a syndesmosis injury.
