After falling to narrow losses in the opening two Tests Wales only had pride to play for in Sydney, but they looked on course to seal a first win over the Wallabies in their own backyard since 1969 when Leigh Halfpenny struck a late penalty, following tries from Ryan Jones and Australia's Rob Horne.
But Berrick Barnes stepped up to break Welsh hearts again with a 75th minute match-winning penalty.
Rob Howley showed faith in the side that crashed to the 25-23 defeat in Melbourne last week, naming an unchanged starting line-up.
Australia were able recall Kurtley Beale. The star full-back had recovered from a shoulder injury and was made available for selection despite being investigated by police for a nightclub fracas ahead of the first Test.
Wales got off to a worrying start at the Allianz Stadium, with the Australians determined to inflict a whitewash on the RBS 6 Nations champions. Sitaleki Timani clattered Halfpenny with a late tackle and Barnes banged over an early penalty.
But the red-hot full-back shook off the knock to level the scores in the eighth minute after the Wallabies were penalised for failing to roll away from a ruck.
The hosts almost instantly responded as Wales were pinged straight from the restart but again Halfpenny hit back with a monstrous shot at goal.
In Melbourne the lead changed hands on 11 occasions and the third and final Test was set to become another thriller with Barnes on target.
Wales were growing in confidence and they surged up field with Jon Davies and giant wings George North and Alex Cuthbert carrying to good effect.
But David Pocock's influence on the game was growing and the Wallabies captain managed to snatch two turnovers in quick succession, as the opportunity was lost.
The Wallabies cleared down field but Sam Warburton proved he was just as potent at the breakdown, stealing possession and breaking clear from deep inside his half.
He was eventually dragged down and Wales hammered at the Wallabies before they settled for a third Halfpenny penalty.
Wales were dealt a major blow shortly before the half hour mark with Warburton forced off to be replaced by Justin Tipuric and Barnes compounded Welsh woes with his fourth penalty to hand the Wallabies a 12-9 lead at the interval.
Wales lost another talisman at half-time as Gethin Jenkins failing to return from the changing rooms with Paul James coming on.
But the enforced change only strengthened the Welsh scrum and they were rewarded with a penalty, which for the first time in Australia Halfpenny failed to convert.
But Wales quickly demonstrated their attacking flair.
Following a Beale chip over the top, North ran the ball back from deep inside his half and linked with Alex Cuthbert, who in turn offloaded to Rhys Priestland.
The fly-half drilled the ball into the corner and Tipuric forced Beale over his own try-line.
Wales dominated a succession of scrums but failed to earn the penalty try they wanted.
They continued to exert pressure and Jones crashed over under the posts following strong charges from Mike Phillips and Cuthbert.
Halfpenny fired over the conversion but Horne hit-back within a matter of minutes, after the Wallabies created an easy overlap.
He missed the conversion and Halfpenny took full advantage with his fourth successful penalty to set-up a nail-biting finale.
But in all too familiar circumstances the Wallabies came fighting back at in the closing stages and Barnes demonstrated his nerves of steel to seal the win.
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