The Reds bagged maximum points against the Chiefs thanks to an impressive 31-23 Super Rugby win in Hamilton on Saturday.
It was the Queenslanders fourth straight victory over their trans-Tasman rivals, and puts them on 31 points in the tournament wildcard places - eight ahead of the fifth-placed Hurricanes.
A day after being left out of Australia's training squad for the British and Irish Lions tour Down Under, Cooper's masterclass performance inspired the Reds to a resounding victory.
Reds winger Rod Davies grabbed a double in his first starting opportunity of 2013 while number eight Jake Schatz and Cooper, who also added 11 points with the boot, crossed for five-pointers.
Not far behind Cooper in the influence stakes was scrum-half Will Genia, who pulled the strings brilliantly behind a dominant Reds pack as the visitors inflicted just the second home loss on the Chiefs in 14 months.
The Reds started the match with a roar and a hiss, with lock James Horwill unlucky not to have scored early on after being held up over the line. Davies then dropped the ball with the tryline begging, but made amends after intercepting an Aaron Cruden pass and raced in for the opening try under the sticks.
Chiefs full-back Gareth Anscombe put his team on the scoreboard with a penalty shot before setting up the hosts' first try when he put centre Bundee Aki over the line.
Anscombe's conversion took the Chiefs out to a 10-7 lead, but once the Reds replied through number eight Schatz's converted try from a driving maul - they never looked back.
That score took the Reds into a deserved four-point (10-14) lead at half-time.
The Chiefs closed the gap to a single point early in the second half thanks to another Anscombe penalty, but that would be the closest the hosts would come to staying in touch with the Queenslanders.
The Reds then scored two quickfire tries that effectively left the Chiefs with a mountain to climb after Cooper dummied his way past Cruden for a solo score before Genia fired a bullet pass to Davies who strolled over untouched out wide.
Trailing 13-28, the Chiefs were in trouble. But the momentum swung in favour of the hosts when replacement Patrick Osborne was brought off the bench and made an instant impact.
Anscombe added another penalty as the Chiefs began to claw their way back and when Reds centre Anthony Faingaa was sin-binned for a ruck infringement, Osborne immediately crossed to slice the gap to eight points.
But the Chiefs were unable to get any closer thanks to some gutsy defence from the visitors. Cooper had the chance to put the result beyond doubt, however missed two penalties in the last 10 minutes of an absorbing encounter.
Tries: Aki, Osborne
Cons: Anscombe 2
Pens: Anscombe 3
Tries: Davies 2, Schatz, Cooper.
Cons: Cooper 4
Pens: Cooper 2
Chiefs: 15 Gareth Anscombe, 14 Tim Nanai Williams, 13 Richard Kahui, 12 Bundee Aki, 11 Asaeli Tikoirotuma, 10 Aaron Cruden, 9 August Pulu, 8 Liam Messam (c), 7 Sam Cane, 6 Tanerau Latimer, 5 Brodie Retallick, 4 Michael Fitzgerald, 3 Ben Tameifuna, 2 Hika Elliot, 1 Toby Smith.
Replacements: 16 Rhys Marshall, 17 Michael Kainga, 18 Nick Crosswell, 19 Fritz Lee, 20 Brendon Leonard, 21 Andrew Horrell, 22 Patrick Osborne.
Reds: 15 Jono Lance, 14 Dom Shipperley, 13 Anthony Faingaa, 12 Ben Tapuai, 11 Rod Davies, 10 Quade Cooper, 9 Will Genia, 8 Jake Schatz, 7 Liam Gill, 6 Eddie Quirk, 5 James Horwill (c), 4 Rob Simmons, 3 James Slipper, 2 James Hanson, 1 Greg Holmes.
Replacements: 16 Albert Anae, 17 Ben Daley, 18 Ed O'Donoghue, 19 Jarrad Butler, 20 Ben Lucas, 21 Chris Feauai-Sautia, 22 Aidan Toua.
Referee: Steve Walsh (Australia)