Wales moved 28-27 ahead with a penalty try 15 minutes from the end and looked on course for their first win over the Wallabies in 10 matches.
But the immaculate Foley calmly slotted over a drop goal and nailed a penalty to give Australia coach Michael Cheika a win in his first competitive game in charge.
"It was a squad effort today," Foley told the BBC.
"The guys were relentless in their efforts and it was a true team effort."
Both sides scored three tries in a fluctuating and expansive first half to leave the scores level at 21-21 at the interval.
Wales scrumhalf Rhys Webb threw a dummy and scampered over to give the hosts an early lead but the Wallabies hit back through Israel Folau.
The fullback then took advantage of an interception to sprint over from 70 metres to put the touring side ahead before George North burst clear for Wales and sent winger Alex Cuthbert over.
Centre Tevita Kuridrani cut through the Welsh defence to restore Australia's lead but Wales lock Alun-Wyn Jones crashed over to complete a frenetic half.
Flyhalf Foley kicked two penalties early in the second half but Wales continued to pour forward and were rewarded when their pack disrupted the Australian scrum to earn a penalty try.
Foley took his personal tally to 18 points in the dying minutes and a furious Welsh onslaught proved futile as the Wallabies struck another psychological blow ahead of next year's World Cup in which both teams are in the same group along with hosts England.
