This game looked a match too far for both teams with mistakes blighting much of the test before a rousing finish at last delivered some garnish.
"They really put in; they were dropping like flies but they stuck to it," victorious Wallaby coach Robbie Deans said.
The injury toll was high. Standout fill-in five-eighths Berrick Barnes said: "We did it tough - it was last man standing".
Wales struggled to kick their goals once more and coach Warren Gatland lamented the injury absence of his five-eighths Rhys Priestland and suspended skipper Sam Warburton. "Without Sam at seven we came up a bit short against [David] Pocock," said Gatland. "But no excuses, they deserved to win."
After Kurtley Beale failed to recover fully from a hamstring strain ahead of the semifinal, there was a feeling his absence harmed the Wallabies more than any other factor in their loss to the All Blacks.
Beale returned last night, but on his first foray he pulled up lame again and was gone after seven minutes.
On the 20-minute mark, Cooper was also gone, damaging his right knee ligaments when he went to step and his limb failed him.
Barnes moved in a place and his calm authority was a major ingredient in the Wallabies' victory.
There had been earlier drama when lock Nathan Sharpe, playing in his 100th test, hurt his knee when his lifters failed to support him in a lineout. He battled on until the 45th minute, but was not in top shape and had to be replaced.
The Wallabies led 7-3 when Barnes scored a converted try in the 10th minute from a scrum move and Hook responded with a penalty for Wales.
The try was textbook timing with the hint of a decoy from James O'Connor stopping the Welsh defence enough for Cooper's pass to hit Barnes in the gap.
The Wallabies had spurned several early penalty attempts in favour of kicking for touch and attacking from lineouts. Their intent was good, but they lacked precision.
Wales felt they had a pack to compete with the best throughout the competition and had concentrated on using a kicking game and Jamie Roberts to punch metres in midfield for some phaseplay rewards.
This time they were not so effective in the scrum with the injury exit of tighthead Adam Jones and the suspension of flanker and captain Warburton.
It was unclear whether either side would deviate from the rigid percentage styles which came up short for them in the semifinals. On the night, both wanted to give the ball more air.
The Wallabies should have sealed the test when they broke late and with some superb interplay Barnes, O'Connor and Anthony Fainga'a put Adam Ashley-Cooper away but he knocked the ball on in George North's great cover tackle.
However Ben McCalman sealed the test minutes later when the Wallabies moved possession and he outflanked the defence.
Wallabies (B Barnes, B McCalman, tries; J O'Connor con, 2 pen, Barnes drop goal)
Wales (S Williams, L Halfpenny, tries, J Hook pen, S Jones pen, con)
Halftime: 7-3
