Filipo Daugunu scored twice with Jake Gordon and Allan Alaalatoa also crossing on a wet and cold Melbourne night to back up their 25-16 triumph in Sydney a week ago.
They took a 23-14 lead into the break and withstood intense second-half pressure and a series of handling errors to seal the series 2-0 and give new coach Joe Schmidt the second win of his tenure.
"It was tough, bit of relief at the end there," said Wallabies skipper James Slipper.
"It was scrappy from us for sure, it wasn't our best game, but we got the result. There's plenty to work on though.
"They are gritty, they hang in there, they played our kicking game really well tonight," he added.
Defeat piled more pain on Warren Gatland's team which is now one loss away from equalling Wales' all-time record of 10 consecutive defeats, which came in 2002 and 2003 under another New Zealander, Steve Hansen.
They have slumped to 11th in the world rankings, below Fiji and Italy.
Despite clawing back from 17-0 down after 25 minutes, they paid the price for conceding too many penalties and again lost the breakdown battle, sorely missing injured workhorse No.8 Aaron Wainwright.
"We never gave up, we had a never-say-die attitude," said Wales captain Dewi Lake.
"But obviously we are a young team and we don't have enough experience really at Test level. What matters is results and we are not giving ourselves those at the moment."
Tense finale
Taine Plumtree assumed Wainwright's role in the back row with James Botham, grandson of England cricket great Ian Botham, starting at blindside flanker and Tommy Reffell at openside.
But they were immediately exposed as Australia scored inside seven minutes with a move that started from near their own try line.
Under pressure, wing Andrew Kellaway sidestepped the Welsh defence then collected his own chip before offloading to a charging Fraser McReight who powered up the field and found Daugunu to finish.
With the rain hammering down, they kept the pressure on with Lolesio making it 10-0 off the tee with a penalty.
Daugunu made a try-saving tackle on Botham as Wales warmed to the task, but it was Australia who scored once more against the run of play.
Scrum-half Gordon sent up a box kick and a handling error from fullback Cam Winnett allowed him to collect it and weave past two defenders to the try line.
Undeterred, a well-worked rolling maul from the lineout saw Lake muscle over to get Wales on the board after half-an-hour.
With Australia's Lukhan Salakaia-Loto in the sin-bin he repeated the feat soon afterwards.
Both tries were converted to get Wales back in the game at 20-14 and an early converted try to veteran winger Liam Williams in the second-half put the Wallabies on notice.
But the hosts proved they too could work a rolling maul, with Alaalatoa powering over.
Daugunu got his second after a schoolboy error from Williams, who tried to keep the ball in play from a Wallabies kick, only to palm it perfectly to a charging Daugunu who surged to the line.
It gave Australia a 33-21 lead, but they went to sleep and Wales winger Rio Dyer smashed over in the corner to set up a tense finale.
