Justin Tipuric and fellow 2009 Lion Alun Wyn Jones followed suit as Wales took control to lead 19-6 at half time.
But the tourists, showing 14 changes from the first Test defeat to the Wallabies last Saturday, were forced to dig deep as the Super Rugby outfit threatened a comeback after the break.
A series of penalties saw Australia's top team cut the gap to four points to test Welsh resolve ahead of Saturday's second Test in Melbourne.
The Brumbies fielded an inexperienced side with eight Wallabies missing but warmed up with pictures of their famous 69-30 win over Wales on the 1996 tour playing on the big screen.
Australia's leading Super Rugby side were playing for places in the final rounds of qualifying for the play-offs which start the week after Wales head home, while the tourists were looking to press their claims for a Test spot against the Lions' next opponents.
Brumbies skipper Zac Holmes got his side off to the perfect start with a penalty after 10 minutes, but Wales grabbed three tries in response to take firm control.
Hook, playing in his favourite position of outside-half, crossed for the first and then combined with Ashley Beck to send back-row Tipuric over for the second.
Hook converted both tries, but couldn't hit the mark from near the touchline after skipper Jones had crashed over on the hooter. Holmes had kicked his second penalty moments earlier, leaving Wales with a 13-point interval lead.
Caretaker Wales coach Rob Howley had called on his players to be more streetwise at the breakdown following their defeat in Brisbane but they conceded a stream of penalties in that crucial area
and were never able to regain their earlier momentum in the second half.
The Brumbies dominated territory and possession after the break and three successive Holmes penalties cut the gap to a single score. It could have been even closer had he not ignored the easiest shot of the night in order to kick to touch.
Waleslost Aled Brew in the first half and then took off his replacement, Alex Cuthbert, after 63 minutes as a precautionary measure. With fellow wing George North fighting to reach full fitness after coming off with a dead leg in the first Test, Wales could ill afford to lose try scorer Cuthbert as well.
Hook steadied the ship with two penalties in the closing 12 minutes and Wales were able to pick up their second win over the Brumbies in four outings since 1978.
Brumbies: Pen: Z Holmes 5
Wales: Tries: J Hook, J Tipuric, AW Jones; Cons: J Hook 2; Pens: J Hook 2