The Wallabies bounced back from their shock defeat to Scotland to down Six Nations champions Wales 27-19 in the first of three Tests in Brisbane on Saturday.
Australia outscored the Welsh three tries to one and take a series lead into next week's second Test in Melbourne.
Inspired by halves Will Genia and Berrick Barnes, the Wallabies were a far different proposition than their stuttering 9-6 loss to Six Nations wooden-spooners Scotland in stormy Newcastle last Tuesday.
Australia dominated the first half and led 10-3 at halftime, stretched their lead to 20-6 early in the second term before Wales fought back to trail 20-19 with 17 minutes left.
But the home side had more left in the tank and finished off with a converted try by centre Pat McCabe in the 67th minute to see off the Welsh threat.
The defeat meant Wales have yet to win in nine Tests in Australia since their only win in Sydney in 1969.
"It was important that we put the Scotland loss behind us pretty quickly and it was important to start the series well with some more tough games to come," Wallabies' skipper David Pocock said.
The Welsh struggled to match Australia's first half intensity and got more into the match in the second half as both teams used their replacements.
"The game was played at a great pace and intensity and we struggled to keep up in the first half," Wales captain Sam Warburton said.
"We have plenty to work on ahead of next week and the best team won today."
The Wallabies ripped into the rucks from the outset to deliver Genia and Barnes quick ball and put the Australian attack on the front foot.
Barnes kicked Australia into the lead with a ninth-minute penalty before Welsh winger Alex Cuthbert saved a certain try.
Cuthbert cut down centre Rob Horne with winger Digby Ioane unmarked outside him before the home side increased their lead.
Blindside flanker Scott Higginbotham powered over in the 16th minute for his first Test try after Ioane jolted the ball clear from Rhys Priestland off a high kick.
Barnes's conversion pushed the Wallabies out to a 10-0 lead and could have stretched their advantage after hooker Tatafu Polota-Nau sent man-of-the-match Genia racing clear only for the scrum-half's kick ahead to go out on the full.
Halfpenny kicked Wales's first points with a 23rd-minute penalty, but the Six Nations champions suffered a blow when winger George North was forced off after 29 minutes with a thigh injury to be replaced by James Hook.
Barnes hit the post with a penalty attempt minutes later as the Wallabies finished the half on top.
The influential Genia gave the Wallabies a flying start to the second half when he darted through an opening and stepped past fullback Hook to score beneath the crossbar in the opening minutes for a 17-3 advantage.
Halfpenny kicked his second penalty to reduce the gap to 11 points before Barnes slotted over a drop goal for 20-6.
Wales brought on three fresh forwards and Halfpenny's third penalty was followed by a converted try to Cuthbert to trail 20-16.
Halfpenny landed another penalty to whittle Australia's lead to one point with 17 minutes remaining.
But the Wallabies hit back when Genia sent Pat McCabe racing over at the angle for Barnes to kick the home side to a 27-19 lead with 13 minutes left and seal the contest.