Australia defended superbly and when they finally built some momentum Welsh indiscipline at the breakdown was punished with three Foley penalties.

A magnificent 13-man defensive effort and another assured kicking display by Bernard Foley earned Australia an 15-6 victory over Wales on Saturday to earn a World Cup quarter-final meeting with Scotland and leave the Welsh to face South Africa.

Both teams had already been assured of progressing thanks to their victories over England, but there was still everything to play for at Twickenham, with the Pool A winners earning an easier route to the final. The losers, even if they get past the Springboks, would probably have to play holders New Zealand in the semi-finals.

The match was effectively decided during a remarkable spell midway through the second half when, despite being down to 13 men after two yellow cards, Australia repelled everything Wales threw at them to protect a six-point lead.

There were no tries in the match but no shortage of intensity.

The first quarter was a fascinating arm-wrestle between two equally matched packs as Australia, so long the world’s whipping boys at scrum time, were full of confidence after their demolition job on England.

Wales edged the early encounters but had only a Dan Biggar penalty to show for their efforts despite territorial dominance in the first 20 minutes.

Australia defended superbly and when they finally built some momentum Welsh indiscipline at the breakdown was punished with three Foley penalties.

Biggar added a second for Wales but then missed one, his first failure in 16 attempts in the tournament, to leave the Wallabies 9-6 ahead at the break.

As the second half unfolded it was Australia who were starting to win the individual battles and another “neck roll” penalty allowed Foley to stretch the lead to six points.

The momentum then appeared to swing back as Australia scrumhalf Will Genia and lock Dean Mumm were sin-binned within four minutes and then key flanker David Pocock was forced off with an injury around the hour mark.

Despite relentless Welsh pressure on the line – including two spurned penalties in front of the posts – and wave after wave of crash-ball charges, Australia repelled every assault and twice managed to hold the ball up when Wales did cross the line.

When the 13-man Wallabies finally earned a penalty after another crunching tackle, the whole team joined in a mass hug in recognition of their monumental effort that everyone in the 81,000 crowd recognized as the key to the match.

A minute later they went the length of the field and earned another penalty. There was no muddled thinking or white-line fever on their side as they calmly opted to allow Foley to slot the kick over for a 15-6 lead which they held to make it 11 successive victories over the Welsh.

Australia defended superbly and when they finally built some momentum Welsh indiscipline at the breakdown was punished with three Foley penalties.