The 28-year-old Giteau, who is moving to France after the World Cup, scored a try and kicked two conversions and a penalty for the home side, who have had an awful season.
But they followed up a 22-14 upset win over table-topping Reds last week with a controlled performance.
"We didn't give away too many penalties in our half, we backed our defence... and the boys worked hard," Giteau said.
"We took our foot off the pedal a little bit but we regrouped and got a couple of tries."
The Brumbies scored three tries in the first half through Christian Lealiifano, Tyrone Smith and Giteau, while Pat McCabe and Moore added second half tries for the home side.
Former England flyhalf Danny Cipriani, who returned to the Rebels' side after being suspended for disciplinary reasons, scored their only points before the break with a penalty.
The Brumbies extended their 18-3 halftime lead shortly after the break when inside centre McCabe ghosted off the shoulder of Moore, who had straightened the attack and burst through, to grab the bonus-point try.
The Rebels then appeared to go into consolidation mode, seemingly content not to let the score blow out before Jarrod Saffy scored one try and set up another for replacement Afusipa Taumoepeau to tighten the game up before Moore barrelled over.
Rebels captain Stirling Mortlock said: "Late in the second half we got a bit better shape and more cohesion in attack, which is the sort of rugby we want to play but it's very disappointing when we don't hold on to possession and our defence was off. It's pretty disappointing really."
Teams
Brumbies:
15 Christian Lealiifano, 14 Henry Speight, 13 Tyrone Smith, 12 Pat McCabe, 11 Adam Ashley-Cooper, 10 Matt Giteau (captain), 9 Patrick Phibbs, 8 Ita Vaea, 7 Julian Salvi, 6 Mitchell Chapman, 5 Mark Chisholm, 4 Ben Hand, 3 Ben Alexander, 2 Stephen Moore, 1 Jono Owen
Substitutes: 16 Anthony Hegarty, 17 Jerry Yanuyanutawa, 18 Peter Kimlin, 19 Henry Vanderglas, 20 Nick White, 21 Robbie Coleman, 22 Andrew Smith
Melbourne Rebels:
15 Mark Gerrard, 14 Richard Kingi, 13 Stirling Mortlock (captain), 12 Julian Huxley, 11 Cooper Vuna, 10 Danny Cipriani, 9 Nick Phipps, 8 Gareth Delve, 7 Michael Lipman, 6 Jarrod Saffy, 5 Kevin O'Neill, 4 Alister Campbell, 3 Greg Somerville, 2 Ged Robinson, 1 Rodney Blake
Substitutes: 16 Adam Freier, 17 Laurie Weeks, 18 Adam Byrnes, 19 Tim Davidson, 20 Lachlan Mitchell, 21 Peter Betham, 22 Afusipa Taumoepeau