The Rebels' fourth win of the season put them top of the Australian conference while sending the rebuilding Reds crashing back to earth after successive wins in their last two matches.
Frozen out by Reds coach Brad Thorn for the entire 2018 season, new Rebels recruit Cooper set up both Maddocks' tries and kicked 12 points against his former team.
The former Wallabies flyhalf cupped his hand behind his ear in a gesture at the crowd before slotting his third conversion after the final siren.
"There's a few people (in the crowd) that feel like I must have left them. But in saying that, it's always like that," said New Zealand-born Cooper, who played 118 games for the Reds.
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"There are some very passionate Reds supporters here."
Hooker Anaru Rangi and replacement flanker Rob Leota grabbed the other tries for the Rebels, who returned to winning ways after a disappointing tour of South Africa.
The Rebels kept the Reds try-less until the 74th minute when replacement prop Taniela Tupou barged over after multiple phases on the goal-line.
"Great win, super proud of the boys," stand-in Rebels captain Angus Cottrell said.
"They were able to grind that out in pretty tough conditions there so just happy to get the win."
Will Genia, reunited with 30-year-old Cooper at the Rebels after forming a dominant partnership with him at the Reds until 2015, wore a big bruise under his left eye throughout but enjoyed an industrious night in greasy conditions behind a dominant forward pack.
"We sort of identified areas of strength of theirs throughout the week and wanted to take that away from them, obviously just their forward dominance and at scrum-time," said the Wallabies scrumhalf.
"You've got to give credit to our forwards."
The Rebels dominated possession and territory in the first half but weren't rewarded until just before the break when Cooper created Maddocks' first try with a pin-point kick to the right corner.
The winger soared high over fullback Hamish Stewart to make the catch and plant the ball over.
Seven minutes into the second half, Cooper capitalised on a turnover at midfield, toeing the ball forward twice to allow supporting runner Maddocks to win a sprint to the line for his second try.
Rangi grabbed his try after peeling off a driving maul near the right corner in the 44th minute, with Leota's 79th minute try giving the Rebels a bonus point as they leapfrogged the New South Wales Waratahs to top spot in the conference.
(Reporting by Ian Ransom; Editing by Christian Radnedge)
