The Rebels dominated territory and possession in the game’s opening half but the two teams traded penalties for a 6-all scoreline nearing the break.
With the half-time siren looming, a pinpoint cross-field kick by Cooper allowed Jack Maddocks to outjump Hamish Stewart and give the Rebels an 11-6 advantage.
After the break, the Rebels capitalised on an early Reds penalty to again hold the territory advantage with Anaru Rangi peeling off the back of a maul to score.
Another Reds error, this time a dropped ball led to a third try for the Rebels in the 47th minute.
Cooper pounced on the loose ball near the halfway line, twice soccering through before Maddocks won the race to extend the lead to 25-6.
The home team thought they’d got one back when Brandon Paenga-Amosa crashed over from close range but a TMO review after the try had been awarded detected a knock-on by Reds halfback Tate McDermott.
The Reds did eventually get a try when Taniela Tupou scored late in the game but the scoring wasn’t done with Rebels substitute Rob Leota capping a 15-phase move to score in the final minute and secure a bonus point.
Fittingly Cooper ended the action with a conversion, giving him a personal points haul of 12 with two penalties and three conversions.
Melbourne host the Sunwolves next week while the Reds are at home against the Stormers.