On a chilly evening, both teams attempted to run the ball early on but it was the home side who took the lead on nine minutes when Zac Holmes booted over the first of his five penalties.
Wales scored their opening try in the 18th minute after quick thinking by scrum half Rhys Webb. The Ospreys halfback took a quick tap and shot down the blindside before off-loading to Hook who plunged over in a tackle. He converted his own try to put Wales in front.
In the first half Wales enjoyed being in charge with Hook floating out passes beautifully with Ashley Beck in particular enjoying the room provided. Wales were also in charge at the breakdown where their physical and aggressive attitude intimidated the home side.
Beck was instrumental in Wales's second try, bursting through a tackle before off-loading to the supporting Tipuric who did the rest. Again Hook added the extras.
Holmes reduced the arrears with another penalty but Wales struck back immediately. Webb again attacked with intent and after several surges by the forwards, Jones powered his way over the try-line.
Paul James replaced Alun Wyn Jones as captain after the second row was replaced by Ospreys colleague Ian Evans at the break. Later in the second half Tipuric took over the captaincy as James was replaced by Rhys Gill.
Tipuric said after the game: "It was fast and very tough at the breakdown tonight - it was great experience for the guys to play against a Super 15 side. We tried to target the breakdown area. It's obviously refereed differently over here and another learning curve for the guys so the win is a great boost for the squad going into the second Test against Australia on Saturday."
Brumbies: Pens - Z Holmes (5)
Brumbies: R Coleman (T Cox 44); C Crawford, T Kuridrani, A Smith, K Sitauti; Z Holmes, I Prior (B Mokotupu 70); R Murphy, A Hegarty (S Siliva 57), S Sio (J-P Pradaud 70), L Power (D Sigg 56), B Hand (capt), P Kimlin, I Vaea (F Auelua 52), C Faingaa.
Wales: Tries - J Hook, J Tipuric, AW Jones; cons - J Hook (2); Pens - J Hook (2)
Wales: Liam Williams; H Robinson, A Bishop, A Beck, A Brew (A Cuthbert 38/Lloyd Williams 63); J Hook, R Webb; P James (R Gill 52), R Hibbard (K Owens 70), R Jones, AW Jones (capt, I Evans h-t), L Charteris, J Turnbull, A Shingler (G Delve 29), J Tipuric.