The Reds recovered from their loss to the Waratahs last week by beating the Cheetahs 43-33 with a bonus point in Brisbane on Friday.
The Reds outscored the Cheetahs by five tries to three with two tries from Reds centre Chris Feauai-Sautia.
The Cheetahs have now played four matches in Brisbane and have yet to win a match in the city.
Quade Cooper kicked a penalty in extra time which cost what would have been the Cheetahs first bonus point in Brisbane.
The result moves the Reds provisionally up to fifth place in the overall standings but third in the Australian Super Rugby conference.
In a remarkable start, the Reds received a penalty try in the first minute and Cheetahs winger Rayno Benjamin was sin-binned for kicking the ball out of Chris Feauai-Sautia's hands as he attempted to plant the ball on the try-line.
But while they were down to 14 men, the Cheetahs crossed twice, with Cheetahs winger Willie le Roux charging down a Will Genia box-kick for center Francois Venter to score, then Reds flyhalf Quade Cooper threw a wayward spiral pass only for Boom Prinsloo to intercept and canter 50 meters.
Cooper redeemed himself by floating another cut-out pass over two defenders. But this time it hit center Mike Harris, who passed to winger Rod Davies, who sped down the sideline for another Queensland try.
The score was 14-14 after 12 minutes, and after a six-try first half the Reds led 29-20.
Feauai-Sautia's second try from a Cooper grubber kick appeared to seal the result for the Reds at 34-23, but Queensland errors led to a third try to the Cheetahs by Elgar Watts, which he converted for them to trail the home side by only seven points with seven minutes remaining.
However, the Cheetahs, after dominating the scrum all game, conceded a scrum penalty in front of their posts in injury time and Cooper kicked the goal after the siren to give the Reds a 10-point edge and prevent the Cheetahs from claiming a bonus point for finishing within seven points of the winners.
Cooper finished with an 18-point haul and became Queensland's highest point-scorer in Super Rugby with 632, three more than Elton Flatley.
"We knew we had to do the hard work first," Cooper said.
"Then we got a bit ahead of ourselves."
Next week the Reds travel to South Africa where they will play the Sharks in Durban while the Cheetahs fly to New Zealand where they will take on the Hurricanes.
Final Score Reds 43 (29) Cheetahs 33 (20)
Tries - Penalty, R.Davies, C.Feauai-Sautia 2, J.Hanson
Pen - Q.Cooper 4
Con - Q.Cooper 3
Tries - S.Venter, B.Prinsloo, E.Watts
Pen - J.Goosen 3
Con - J.Goosen 2, E. Watts
Cards - R.Benjamin (1st min yellow)
Referee: Garratt Williamson
Assistant Ref 1: Angus Gardner
Assistant Ref 2: Matt O'Brien
TMO: Steve Leszczynski
1. Ben Daley , 2. James Hanson , 3. Greg Holmes , 4. Rob Simmons , 5. James Horwill (C) , 6. Eddie Quirk , 7. Liam Gill , 8. Jake Schatz , 9. Will Genia (VC) , 10. Quade Cooper , 11. Dom Shipperley , 12. Mike Harris , 13. Chris Feauai-Sautia , 14. Rod Davies , 15. Aidan Toua
Replacements : 16. Saia Fainga'a , 17. James Slipper , 18. Jono Owen , 19. Ed O'Donoghue , 20. Beau Robinson , 21. Nick Frisby , 22. Anthony Fainga'a , 23. Ben Tapuai
15 Hennie Daniller, 14 Rayno Benjamin, 13 Johann Sadie, 12 Francois Venter, 11 Willie le Roux, 10 Johan Goosen, 9 Shaun Venter, 8 Philip van der Walt, 7 Lappies Labuschagne, 6 Boom Prinsloo, 5 Francois Uys, 4 Lood de Jager, 3 Maks van Dyk, 2 Adriaan Strauss (captain), 1 Caylib Oosthuizen.
Replacements :16 Ryno Barnes, 17 Trevor Nyakane, 18 Rossouw de Klerk, 19 Ligtoring Landman, 20 Jean Cook, 21 Sarel Pretorius, 22 Elgar Watts, 23 Cornal Hendricks