Boks made a 'last stand' at Twickers
Wales were leading 19-18 when the 33-year-old veteran Du Preez darted down the blindside and over the line for the match-winning points five minutes from the end.
South Africa then held off a late Welsh onslaught to reach the semifinals – where they will meet New Zealand next week.
"It was a tough game, they came hard at us," Du Preez said.
"We just said to ourselves 'keep pushing, keep pushing'.
"At one stage I saw some of the guys lying down and I told the guys 'look we have to go and fight now' and the guys produced."
It was a remarkable result for the two-time world champions who have vowed to win the trophy despite no side ever winning the title having lost a pool game – they were on the receiving end of the greatest upset in World Cup history in the opening game, a 34-32 defeat to Japan.
"We have learned from the Japan game, it is part of who we are now," said the captain.
Du Preez said the team's "character" and maybe "a real blessing from above" had helped.
Wales coach Warren Gatland was downcast.
"At the start the boys gave everything. They just weren't good enough to hang on in the last few minutes," the New Zealander said.
Gatland would not use the team's heavy injury toll as a cause for the defeat.
"I don't want to make any excuses. At the end of the day South Africa won the game. We weren't good enough to win
"South Africa did what South Africa do. They hung in there right until the 80 minutes. They got one chance and they took it and that was the result."
He said a lot of the players would come back stronger when Wales tackle the Six Nations in early 2016 and they go on a tour of New Zealand.
Agence France-Presse
