Wales made 14 changes from the team that lost the first Test in Brisbane four days earlier and seemed to be in control at the break after scoring three tries.
But the home side rallied in the second half and cut the gap to four points heading into the final quarter to test the Welsh resolve ahead of Saturday's second Test in Melbourne.
The Brumbies were without eight Wallaby squad members and, despite being the top Australian team in the Super Rugby ratings, chose to field a pretty inexperienced side. There were 10 players with fewer than 12 Super Rugby appearances in the home side's ranks.
But the locals warmed up with pictures of the Brumbies famous 69-30 win over Wales on the 1996 tour and were playing for places in the final rounds of qualifying for the Super Rugby play-offs which start the week after Wales head home.
Brumbies skipper Zac Holmes got his side off to the perfect start with a penalty after 10 minutes, but Wales managed to grab two 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 Justin Tipuric over for the second.
Hook converted both tries, but could not hit the mark from near the touchline after skipper Alun Wyn Jones 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 the 27-19 first Test 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 four points. It could have been even closer had he not ignored the easiest shot of the night in order to kick to touch.
Wales lost Aled Brew in the first half and then took off his replacement, Alex Cuthbert, after 63 minutes as a precautionary measure.
With 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.
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