South Africa have come out on top in 28 of the 35 matches played between the two countries but Wales' six wins include all four games played since they narrowly lost the 2015 World Cup quarter-final.
Here the PA news agency looks ahead to the second semi-final and reflects on England's thrilling victory over reigning champions New Zealand.
Gatland happy with underdog tag
Wales are Six Nations Grand Slam champions and were the world's number one team only a few months back according to the world rankings.
But they scraped into the last four by beating 14-man France 20-19 and have yet to hit their best form in Japan, while the Springboks' star has been on the rise this year.
South Africa have lost only once in 10 games – the 23-13 World Cup pool defeat to New Zealand – and go into the game as favourites.
Gatland, whose 12-year reign is drawing to a close, said: "The nice thing about being out here is that you are kind of in a bubble and you are not seeing a lot of the stuff externally.
"It does get us up when people write us off. If they continue to do that over the next couple of days that would be brilliant.
"I can't understand why people would write us off when our record against South Africa has been pretty good in the last four or five years. That speaks for itself."
Wales have lost both of their World Cup meetings with South Africa, although the total margin of those defeats adds up to just five points.
South Africa won a 2011 pool game 17-16 in Wellington, and Fourie Du Preez's late try saw the Springboks edge home 23-19 in the last eight at Twickenham four years ago.
"We were quite unlucky to lose that quarter-final four years ago," said Wales scrum-half Gareth Davies, who is set to win his 50th cap on Sunday.
"We were devastated with that because we felt we deserved to win that game.
"We feel like we owe them one for four years ago. That will be in the back of our minds and hopefully we can get one over them."
Springboks preparing for wet-weather rugby
Rain is expected for the showdown and the Springboks have named a six-two split of forwards and backs on the bench.
Fly-half Handre Pollard said: "We don't select our team based on the weather, but going with the six-two split certainly helps when it's wet.
"It's going to be a big set-piece battle and gain-line battle, whether it's dry or wet. We have prepared for that.
"Our game plan suits dry and wet weather pretty well, so there won't be any major adjustments because of the weather."
England focused on final
England boss Eddie Jones refused to bask in the glow of releasing New Zealand's grip on the World Cup.
The All Blacks were aiming for a hat-trick of triumphs, but England shot them down with a fully-deserved 19-7 victory in Yokohama.
"We're here for another week – and we know we can play better next week," Jones said. "We've got the right focus.
"We set out four years ago, the meeting at Pennyhill Park, our first meeting together. We wanted to be the best team in the world and we're not the best team in the world.
"But we've got an opportunity to play in a game where we could be and that's the only thing we're concerned with."