Japan will be in their first Olympic final against the US, who they beat on penalties in last year's World Cup final, after the Americans snatched an astonishing 4-3 extra-time win over neighbours Canada at Old Trafford in the late game.
After a quiet opening half-hour the first semi-final came to life when Yuko Ogimi gave Japan the lead and it continued to enthrall a crowd of 61,482 right to the nerve-jangling finale in what was an outstanding advertisement for the women's game.
Ogimi scored when she scrambled the ball home after French keeper Sarah Bouhaddi fumbled a long free-kick from Japan skipper Aya Miyama after 32 minutes.
Japan doubled the lead with a well-directed header from Mizuho Sakaguchi in the 49th from another Miyama free-kick.
France, who never stopped attacking and generally played the better football, finally Broke through in the 76th with a brilliantly-executed volley from substitute Eugenie Le Sommer.
Three minutes later they had the chance to equalise with a penalty but Elise Bussaglia fired wide. Only desperate, last-gasp defending and outstanding saves from Japan goalkeeper Miho Fukumoto kept France out.
Japan had the chance to wrap up the win in added time when Ogimi, running through with only Bouhaddi to beat, hit the post but they held on for a win that puts them into the Olympic final for the first time.
Japan coach Norio Sasake said: "It was just a small difference that helped us win the match, perhaps we were just that bit stronger mentally.
"But we were inspired before the match by a wonderful speech from Miyama in the dressing room that almost made me cry.
"She said she was honoured to play here with these players in this stadium, and that was very inspiring for us."
France had beaten Japan 2-0 in a friendly in Paris just before the Olympics but Sasaki said he learnt enough from that defeat to counter their tactics at Wembley, preventing wing back Wendie Renard from creating anything for her side.
"The tactics worked, and we stopped her from being too dangerous, she didn't create anything," he said.
Japan's men's team will try to match the women's achievement when they play Mexico in their semi-final on Tuesday.
France coach Bruno Bini said the defeat to Japan was even tougher to take than the defeat by Sweden in last year's World Cup semi-finals but he still managed a joke.
"I'm not very good at semi-finals," he said, "I lost last year and lost today, so if we reach the semi-finals of the European Championships next year, I will go home and give the team to someone else to look after."
France, who finished fourth in last year's World Cup, will get the chance of an Olympic bronze in their first appearance in the tournament, when they face Canada in the third-place play-off match at Coventry on Thursday.