They arrive in the knockout phase battle-hardened by intense Pool A showdowns with England, Fiji and Australia, losing only to the Wallabies in a thunderous collision last weekend.
Four years ago Wales were edged 9-8 by France in the semi-finals, a match that saw captain Sam Warburton controversially sent off for a spear tackle, and Gatland insists there is unfinished business in the World Cup.
“Coming out of our pool was tough and to beat South Africa to reach the semi-finals would be an awesome achievement,” the head coach said.
“And the beauty of that is that we’d be here until the end of the tournament as well. We’re not ready to go home on Sunday. The players aren’t ready to go home.”
The Springboks, who enter the last eight clear favourites, will be wary after Gatland revealedWales will have a surprise in store at Twickenham.
“What we learned from 2011 is that during this tournament you have to be prepared to throw something different in,” Gatland said.
“We did that against Ireland in 2011 and changed the way we wanted to play. You have to be prepared to do something different.”
Meanwhile JP Pietersen insists South Africa try machine Bryan Habana is improving with age as the wings prepare to spearhead the Springboks’ assault on Wales at Twickenham.
Pietersen has recovered from the knee injury that forced him to miss the 64-0 rout of USA in time for the first World Cup quarter-final and features in the same starting XV as Habana for a 42nd international.
Habana, 32, is the joint highest try-scorer in the World Cup history with 15 and needs just one more to elevate him above New Zealand great Jonah Lomu.
“Bryan gets better as he gets older. He has 114 caps and he’s a legend around South Africa,” Pietersen said.
“When we need something big, Bryan Habana always steps up. To be equal try scorer with Jonah Lomu is a seriously amazing achievement.”
South Africa have nudged their quest to win a third World Cup back on track since being stunned by Japan, stringing together emphatic victories over Samoa, Scotland and the USA.
“It has been difficult for us as a team after what happened in our first game against Japan. It’s been a character test for us,” Pietersen added.
“We’ve played knockout rugby from game two of the pool stage.
“I think that probably helps a lot with the mental preparation for this stage.
“It was definitely emotional after the Japan game. We opened up and had a hard session with ourselves and what we did wrong.
“We let ourselves down and our country down. That’s part of rugby. It’s all about testing the character and our character has been tested since game two.”