The Australia fly-half, who is to move to Toulon after the World Cup, scored a try, had a hand in three others and landed two conversions and a penalty in his final home appearance.
Giteau outshone the returning Rebels and England fly-half Danny Cipriani in the rout - with the Brumbies picking up the bonus point shortly after the break.
Giteau provided the scoring passes to Christian Lealiifano, Tyrone Smith and Pat McCabe, while Stephen Moore also crossed for a try.
"I think it's just nice for the group... achieving something we can be proud of going into the back end of the season," Giteau said.
"We didn't just want that Reds win, we wanted this one as well. We wanted to finish the season on a high."
Cipriani returned from his club ban to score two conversions and a penalty, with Jarrod Saffy and Afusipa Taumoepeau scoring consolation tries in the second half.
Rebels captain Stirling Mortlock, who played 13 seasons for the Brumbies, was left with mixed emotions in the aftermath of the loss.
"I've a lot of memories and a lot of mates here (in Canberra)," he said.
"Disappointing that we couldn't get one over them tonight but nonetheless there's a lot of guys who have put in a lot of years for this club and it's good to see those guys go off with a victory."
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