Wales had looked on course for a series-levelling success in Melbourne thanks to some fine kicking from Leigh Halfpenny, only to miss out in agonising fashion.
Wales got off to a great start, launching a sustained attack after just three minutes which ended when George North side-stepped past Wycliff Palu and Rob Simmons to touch down.
Halfpenny kicked the easy conversion but the hosts went on to have the better of the half and Berrick Barnes kicked a pair of penalties to reduce their deficit to 7-6, before Rob Horne cruised over the line after a clever Barnes dummy.
The Welsh trailed 13-7 at the break but again started the half well, Ashley Beck and Jonathan Davies hacking the ball forward when Will Genia's pass went astray in midfield before Davies grabbed the ball near the line and scored.
Barnes booted a pair of three-pointers either side of a Halfpenny penalty to put the hosts back in front but they then lost Cooper Vuna to the sin-bin for tackling Halfpenny in the air.
The Welsh full-back kicked the resulting penalty to put them up 20-19 but the Wallabies went straight onto the attack and Barnes made it 22-20 when Wales infringed at a ruck.
The reliable Halfpenny was on target once again when Ben Alexander was penalised at a scrum 13 minutes from time and Barnes then put a kick wide of the posts with six minutes left.
But the Wallabies got another chance when, with the 80 minutes having elapsed, Richard Hibbard infringed at a driving maul, and Harris calmly stepped up to drill a tricky penalty straight through the uprights.
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