Defending champions South Africa twice came from behind to overcome France in a pulsating encounter and secure a semi-final date with England back at the Stade de France next Saturday.
The hosts made a blistering start with an early try from prop Cyril Baille but they failed to deal with two high kicks as first Kurt-Lee Arendse sprinted to the corner before Damian de Allende plunged over to give the Springboks a 12-7 lead.
France drew level with a try from hooker Peato Mauvaka, Cheslin Kolbe charging down the conversion from Thomas Ramos before the South Africa wing raced onto Jessie Kriel’s deft grubber to score, only for Baille to grab his second try and Ramos to land a penalty – for a high tackle by Eben Etzebeth which earned the second-row a yellow card – to give Les Bleus a 22-19 interval lead.
Ramos extended their advantage with a penalty, but Etzebeth stretched over with 14 minutes left, replacement Handre Pollard converting and adding a penalty which proved decisive despite a late reply from Ramos.
"I just thought we really wanted it," said Springboks captain Siya Kolisi. "We knew how tough it was going to be. I must give credit to the guys that came off the bench, they came and made a huge difference.
"And most importantly, the people back at home. Honestly, the support that we've received. You know, they can't afford to be here but the videos, the schools singing for us and the videos.
"We play for the nation, it's not about us on this field any more, it's about the people back home and that's what's driving us."
Kolisi paid tribute to France for their display in a heart-breaking defeat in front of their home fans.
The flanker added: "It was a hard game. We knew how tough it was going to be with the French team at home and honestly, I just want to say well done to them for what they've achieved and how hard they've worked."
Kolisi went off early in the second-half but urged his team to victory that keeps alive their hopes of defending the title they won in Japan four years ago.
"Obviously, somebody else was on the field, all I could do was bring the energy. With the amount of French people in the crowd, the boys need all the energy," he added.
South Africa's hooker Mbongeni Mbonambi, named the Mastercard Player of the Match, said: "We knew it wasn’t going to be easy playing the host team in their backyard, sold out crowd singing their national anthem the whole time.
"We’ve still got two more games to go, this is still nothing. We were just focused on what we had to do, we stayed on task. It was a great game of rugby."
Jacques Nienaber, South Africa's head coach, is relishing the prospect of facing England back at Stade de France next Saturday.
"Massive. I think it’s going to be a nice challenge," said Nienaber. "In knockouts anything can happen, like tonight I followed the England game when we were on the bus here.
"They had a healthy lead and then Fiji came back and then they also pushed it right to the end. I think knockouts are going to be small margins right to the end."
"Credit to the French. We knew it was going to be this tight. I think everybody knew it was going to be a big battle. Two good teams and unfortunately, or fortunately for us, we were on the right side of things.
France's team manager Raphael Ibanez admitted being unable to convert several try-scoring opportunities proved costly as their hopes of winning the trophy for the first time were dashed.
"We are very sad tonight," said Ibanez. "I think we gave everything to win that game. We knew it would be a very tight game and we had to score every opportunity. We had some good opportunities but unfortunately we couldn't convert them into points."
"We had our chances, they were pragmatic and sometimes we try and try our best with the support of the French fans. This is why we are sad tonight, we are sad for them.
"We have to get up and stand up and go for the next fight. We have other games coming, not in this World Cup, but we have to still believe in the team."
