The NRL's two most prolific attacking teams were left undermanned by State of Origin selections and consequently underwhelmed with the football for most of Sunday afternoon's game at Allianz Stadium.
Written off before kick-off and without six of their Origin stars, the Cowboys fell behind 16-4 in the second half before clicking into gear, Drinkwater hoisting them to a third consecutive win by scoring a second-half try and kicking the winning penalty goal.
When star second-rower Heilum Luki went to the sin bin for up-turning Sitili Tupouniua early in the second half, it appeared a foregone conclusion the premiership heavyweight Roosters would go on with the contest, after Sam Walker had starred to put them on top.
Instead, Luki's moment of madness appeared to galvanise the visitors, who marched upfield only minutes later to begin closing the gap.
Having sent Braidon Burns over for the Cowboys' first try with a cut-out pass, Drinkwater scythed past Michael Jennings for a slick individual try down the Cowboys' left edge.
When Kulikefu Finefeuiaki bulldozed past Jennings and Walker, Drinkwater had the chance to put the Cowboys in front, only to hook his relatively simple conversion attempt to the left of the upright. The scores were locked at 16-16.
The Roosters lost James Tedesco on game day, called in to replace the injured Dylan Edwards in NSW camp, and struggled for polish in the inspirational captain's absence.
Tedesco's replacement Joey Manu switched from the centres to fullback at the 11th hour but could not replicate the attacking spark that has typified his previous spells deputising at the back, with only Walker proving a constant threat.
Dom Young had a night to forget on the left wing.
The star recruit produced an almighty brain-snap to offload the ball coming out of trouble with the scores tied late, with Manu bundled into touch as he attempted to clean up the scraps.
While the Cowboys were attacking his side's line, Junior Pauga rushed out of the defence and gave away an offside penalty that allowed Drinkwater to seal the game with a conversion attempt. He did not miss this time.
Luki is likely to face scrutiny from the match review committee, with Roosters veteran Jared Waerea-Hargreaves a chance to join him on the charge sheet.
The prop went on report in the first half for putting a high shot on Cowboys lock Thomas Mikaele, and could spend time on the sidelines regardless of any charge. The 35-year-old reported tightness in his right hamstring in the first half and did not return from his first stint.
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