The Reds survived a scare from the Highlanders by hanging on to win 19-13 and keep their Super Rugby title defence alive for another week.
The Reds were outscored by two tries to one with Mike Harris' boot being the difference in the Highlanders final Super Rugby match of the season as they have a bye next week.
The result drops the Highlanders out of contention for the Super Rugby play offs and provisionally moves the Reds back into the top six.
A loss could have dropped the Reds to eighth place overall.
Cooper, growing in confidence in his fourth match back from knee surgery, was a standout to indicate he's back near the form which took the Reds to last year's title.
He regularly took on the advantage line, muscled up in defense and threw some signature spiral passes that put his teammates into space.
The goalkicking of Mike Harris, who slotted five from six, was also crucial for the Reds as they scored one try to the Highlanders' two.
The Reds looked like easy winners when James Slipper was rewarded for a strong display with a 57th-minute try in the right corner for a 16-3 lead.
But the Highlanders came back with tries to Adam Thomson and Chris King following concerted pressure to close the gap to six points with six minutes left.
The Reds defended desperately on their own try-line in the final frenetic minutes as New Zealand's Highlanders tried to find an opening.
But as Highlanders skipper and prop Jamie Mackintosh wrestled his way close to the try-line blindside flanker Jake Schatz won a crucial turnover to protect the Reds' lead and keep them in the hunt for the top-six playoffs with their fifth straight win.
The Reds climbed into sixth place ahead of the weekend's remaining games with their Australian derby against the New South Wales Waratahs in Brisbane next week to decide their play-off fate.
"It was very tough and we made it very hard for ourselves at times and credit to the Highlanders, they put a lot of pressure on us with their pick and go," Reds' skipper Will Genia said.
"It's a massive game for us next week against the Waratahs, our season is on the line so we have to prepare as good as we can and put in a good performance next Saturday."
It was a disappointing finish to the season for Highlanders and their veteran All Black scrum-half Jimmy Cowan, who is leaving to play in England for Gloucester.
"It was a pretty frustrating way to end the game and we got pretty close and to be involved in that turnover is not good," Mackintosh said.
"We would have loved to send Jimmy off a winner. He's played 50 games for the All Blacks and 100 for the Highlanders and what a career he's had."
Final Score Reds 19 (6) Highlanders 13 (3)
Tries - J Slipper
Pen - M Harris 4
Con - M Harris
Tries - A Thomson, C King
Pen - M Delany
Referee: Jonathan Kaplan
Assistant Ref 1:Ian Smith
Assistant Ref 2:James Leckie
TMO : Steve Lesczcynski
1. Greg Holmes,2. Saia Faingaa,3. James Slipper,4. Rob Simmons,5. Adam Wallace-Harrison (vc),6. Jake Schatz,7. Beau Robinson,8. Scott Higginbotham,9. Will Genia,10. Quade Cooper,11. Chris F'Sautia,12. Mike Harris,13. Anthony Faingaa,14. Dom Shipperley,15. Luke Morahan
Replacements : 16. James Hanson,17. Ben Daley,18. Radike Samo,19. Jarrad Butler,20. Ben Lucas,21. Ben Tapuai,22. Nick Frisby
15. Ben Smith, 14. Kade Poki, 13. Siali Piutau, 12. Phil Burleigh, 11. Hosea Gear, 10. Mike Delany, 9. Jimmy Cowan, 8. Nasi Manu, 7. James Haskell, 6. Adam Thomson, 5. Nick Crosswell, 4. Josh Bekhuis, 3. Ma'afu Fia, 2. Andrew Hore, 1. Jamie Mackintosh (c).
Reserves: 16. Jason Rutledge, 17. Chris King, 18. Jarrad Hoeata, 19. Tim Boys, 20. Aaron Smith, 21. Chris Noakes, 22. Kenny Lynn.