"I'm so proud of the boys," new skipper Cordingley said.
"They've copped a lot in the last few weeks. I just asked them to trust each other. That's probably one of our best performances in a long time."
Winger Clinton Schifcofske finished with a career-best haul of 20 points, including a 52nd-minute try when Springbok winger Bryan Habana fumbled a kick.
The Bulls scored only one try -- by Fourie du Preez -- with fly-half Derick Hougaard landing a penalty goal.
It was a dreadful start to their Australasian tour for the Bulls, who slumped to a losing 2-3 record this season and are off to face the Waikato Chiefs in Rotorua next Saturday.
"We've been hearing all this year about Pretoria. In the back of our minds this was payback," said Reds coach Phil Mooney, who made six changes to the lineup that lost its prior game to the previously last-placed Stormers.
"When we got in front, we really went to grind them down. We enjoyed that."
"Right from the kickoff, our young guys aimed up - pushed around the Bulls forwards and showed we were here to play. It was a real turning point for us."
Fourie du Preez, who scored the Bulls only try, said the game was even at halftime.
"We had a lot of opportunities, we just couldn't convert," he said.
"Full credit to the Reds - they played with a lot of heart tonight."
Pen - Clinton Schifcofske (3)
Con- Clinton Schifcofske (3)
Pen - Derick Hougaard
Cards - Derick Hougaard (yellow)
1. Greg Holmes,2. Sean Hardman,3. Dayna Edwards,4. Van Humphries,5. James Horwill,6. John Roe,7. Poutasi Luafutu,8. Leroy Houston,9. Sam Cordingley (c),10. Quade Cooper,11. Peter Hynes,12. Berrick Barnes,13. Morgan Turinui,14. Clinton Schifcofske,15. Chris Latham
Reserves: 16. Stephen Moore,17. Rodney Blake,18. Ed O'Donoghue,19. David Croft,20. Ben Lucas,21. Brando Va'aulu,22. Scott Higginbotham.
Morne Steyn, Akona Ndungane, JP Nel, Wynand Olivier, Bryan Habana, Derick Hougaard, Fourie du Preez (capt), Pedrie Wannenburg, Wikus van Heerden, Danie Rossouw, Wilhelm Steenkamp, Bakkies Botha, Rayno Gerber, Derick KuŁ,n, Gurthro Steenkamp.
Replacements: James vd Walt, Werner Kruger, Dean Greyling, Deon Stegman, Dewald Potgieter, Heini Adams, Stephan Dippenaar.