The reliable Berrick Barnes capitalised on Wales errors as the fly-half kicked 15 points to extend Welsh hurt against Australia in Australia to 43 years.
Ryan Jones had powered Wales into a lead with a pushover try after Mike Phillips dented the Aussie defence.
But Australia hit back on the break as Rob Horne, on the overlap, dived over.
The recalled Kurtley Beale rampaged into the Wales half to feed Digby Ioane but when the first surge was halted, the Wallabies took advantage of the overlap as Horne scored in his second successive Test.
Barnes missed the conversion but a late penalty from the fly-half ensured he out-scored kicking rival Leigh Halfpenny by a point to win the three-Test series 3-0.
And for the second consecutive week, an Australian boot broke Welsh hearts as Barnes cooly slotted over as Wales were penalised at the breakdown with five minutes remaining.
Wales’ one-point reverse against the Tri Nations champions is their narrowest losing margin in Australia but the tourists, who have only beaten the Wallabies once in their own back yard, felt this was a series where they could end their southern hemisphere hoodoo.
Welsh ill-discipline gifted Australia cheap points and that proved the downfall of a Wales side that have now lost their last seven games against the two-time World Champions.
Barnes and Halfpenny traded penalties in a first-half war of attrition but Wales’ penalty count of eight in the first-half speaks volume of their Achilles heel.
Wales also lost their inspirational captain Sam Warburton just before the half-hour clutching his troublesome shoulder as he was forced off but replacement openside Justin Tipuric continued to impress.
The visitors could have gone in at half-time level but Rhys Priestland skewed a 40 metre drop-goal well wide.
Wales lost another talisman at half-time as Gethin Jenkins failed to return and was replaced by Paul James.
Halfpenny almost tied the scores after the break, however the superb Wales full-back missed his only kick of the series – but only just as his giant knock bounced off the upright after Australia were penalised for wheeling a scrum.
Wales, though, gained a sight of the Australian line when after a Beale chip over the top, George North ran the ball back from deep inside his half and linked with Alex Cuthbert, who in turn offloaded to Rhys Priestland.
The Wales fly-half kicked the ball into the corner and Tipuric’s pace forced Beale over his own try-line.
Wales dominated a succession of scrums but failed to earn the penalty try they wanted.
But their continued pressure was rewarded when Jones, in for injured number eight Toby Faletau, crashed over under the posts following a strong charge from Phillips and Alex 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 Barnes, Australia’s fourth-choice number 10, continued his stranglehold on Wales as his penalty extended Wales’ poor record to just two wins over a Tri Nations super-power in their last 40 attempts.