The Six Nations champions are underdogs for the last-four showdown in Yokohama City, where they will be striving to reach the final for the first time.
Wales left it late to beat 14-man France at the quarter-final stage last weekend and must do without full-back Liam Williams (ankle) and flanker Josh Navidi (hamstring) against the Springboks.
Centre Jonathan Davies has been passed fit after a knee problem, though, and head coach Gatland is optimistic his side can defy the odds to earn a shot at the Webb Ellis Cup.
"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." Gatland said.
Even though Wales have got the better of the Boks more often than not in recent years, Gatland is not blind to the fact there are some who dismiss his team's chances of going any further in this tournament.
"If they continue to do that over the next couple of days that would be brilliant. Please continue to do that as it does get us up when people write us off," Gatland said.
"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.
"Going into Sunday’s game it is going to be a tight game and we saw that the first half in South Africa v Japan was a tight game. It will probably be a kicking fest, they kicked 30 times against Japan so we just have got to handle their game.
"It won't be the prettiest game in the world, it will be a tight Test match with probably teams playing for territory depending on what the weather is like."
"When you want something bad enough - and you really, really want it - it can happen..."
Warren Gatland had a lot of meaningful words to say at today's press conference. #RWC2019 pic.twitter.com/jEEoHso3zt
— Welsh Rugby Union (@WelshRugbyUnion) October 25, 2019
South Africa director of rugby Rassie Erasmus, who replaced wing Cheslin Kolbe (ankle) with Sbu Nkosi, is well aware of the threat Wales will pose but says the Rugby Championship holders are ready to send them packing.
"Wales are the reigning Six Nations champions and apart from three defeats in their Rugby World Cup warm-ups, they have put together a really good sequence of results. But we've also found some rhythm and we’ll be ready for the challenge." said Erasmus.
"We have been working hard for 18 months to put ourselves in a position to win the Rugby World Cup and that opportunity is now just 80 minutes away. These players have worked with unbelievable energy to get Springbok rugby back into this position and I know they will leave nothing out on the field on Sunday."
PLAYERS TO WATCH
Wales – Leigh Halfpenny
Halfpenny has started only one game in the tournament, against Uruguay, and played barely 20 minutes in his other appearance off the bench in the hammering of Georgia. The full-back will be tested under the high ball on Sunday, and Wales will need the 30-year-old to draw on all of his vast experience and skill in an unexpected start as he replaces the injured Williams.
South Africa – Faf de Klerk
De Klerk was named man of the match for a typically influential quarter-final performance against Japan. The scrum-half was a bundle of energy in defence and attack, and the Wales forwards must try to prevent the pivot from getting quick ball.
Photo Getty Images Caption: Wales coach Warren Gatland