A stunning show of second-half defence helped Australia to win Rugby World Cup Pool A with a 15-6 win over Wales at Twickenham.

The two sides went into Saturday's encounter knowing victory would see them avoid South Africa in the quarter-finals and set up a last-eight clash with Scotland.

Australia had the better of a tightly contested first half but appeared set for defeat when they saw scrum-half Will Genia and lock Dean Mumm sin-binned in the space of three minutes after the interval.

Despite being reduced to 13 men, Australia stood firm against incredible pressure on their line from Wales, denying Wales beyond the tryline on three occasions.

The boot of Bernard Foley finally settled a thrilling encounter and ensured Australia a return to Twickenham versus Scotland next weekend.

Wales now face the daunting task of trying to seal a second straight win over South Africa after beating them in November last year having previously lost their last 16 matches against the Springboks.

Dan Biggar slotted over a fourth-minute penalty, but Australia eventually began to dictate matters in the breakdown and in the scrum and levelled matters in the 24th minute thanks to a Foley kick.

Further pressure from Michael Cheika's men allowed them to take the lead through Foley, but their advantage did not last long as Biggar nailed a three-pointer from long range three minutes later.

Again Wales' indiscipline inside their own half proved costly as Foley restored Australia's advantage with a penalty from out wide following foul play from Taulupe Faletau.

Biggar missed for the for the first time in the tournament a minute before half-time, but Australia failed to capitalise, Matt Giteau's effort from 57 metres falling short.

Australia remained in the ascendancy in the second half and Foley gave the Wallabies breathing room with a simple penalty due another indiscretion from Faletau, who was penalised for a neck roll.

However, the game appeared to turn in Wales' favour as Genia first saw yellow for tripping and Mumm each saw yellow.

First Genia was sent to sin bin for preventing Gareth Davies - who had earlier charged down a clearing Foley kick to give Wales territory - from taking a quick-tap penalty.

Faletau was then ruled by the TMO to have fumbled the ball over the line before Mumm followed Genia to the bin for an infringement in the line-out.

Sensational defence from Australia stopped George North from finally capitalising on Wales' extra men following quick hands from the backline, and Jamie Roberts was too held up as the Wallabies showcased remarkable resolve.

When restored to 14 men, an excellent Adam Ashley-Cooper tackle as Wales looked to spread it wide once more allowed the Wallabies to win a penalty at the breakdown and clear for territory.

Foley slotted over his fifth penalty from in front to give the Wallabies an decisive nine-point lead, with his late miss after Alex Cuthbert saw yellow for a deliberate knock-on proving immaterial.