Surprise starter Nahomi Kawasumi had two goals for Japan, which will face the United States in Sunday's championship.
It's the first World Cup final for the rising soccer power.
Sawa made an uncharacteristic error in the 10th and fed a defensive pass straight to Josefine Oqvist. She gladly took it, ran through the defense and got a lucky deflection to bury the ball past goalie Ayumi Kaihori.
Kawasumi had just played 29 minutes in the tournament before coach Norio Sasaki started her in Japan's biggest game ever.
"She is very tough and fit," he said. "I didn't ask her to score two goals but she did an excellent job."
In a battle of Japan's fine skills against the thrust and hustle of Sweden, the match turned in the second half when Kawasumi caught Hedvig Lindahl off her line.
Kawasumi lobbed it over her from about 110 feet away for the final score, one of the best in a tournament full of excellent strikes.
Sawa's goal also gave her four for the tournament to tie her with Brazil's Marta. Sawa, though, still has one game left to become the top scorer of her fifth World Cup.
The Japanese players always had more on their minds than their next game in the marquee event for women's soccer. In the wake of the March 11 tsunami and earthquake, they wanted to provide a feel-good story for fans back home.
And they came through.
Following their latest win, they again unfurled a huge banner that said "To our Friends Around the World -- Thank You for Your Support," referring to the global outpouring of aid after the tsunami, that left nearly 23,000 dead or missing.
"What we have been doing so far is very good for Japan," Sasaki said. "We are still recovering from the disaster. There were so many victims," he said.
"Even little things, like a win can give people courage and hope."
When Japan faced favored Germany in the quarterfinals, Sasaki showed her players heart-tugging pictures from the victims of the tsunami shortly before the game to give them more resolve.
He didn't need the tactic Wednesday; his team had enough determination to overcome an early mistake by one of its best players.
Team captainMany in the crowd of 45,434 at Commerzbank Arena thought Sweden would use its vast experience to control the play once it got the lead.
Turns out Japan was ready.
Japan tied it nine minutes later when Kawasumi somehow got a foot on a cross from star Aya Miyama and pushed it through the legs of goalkeeper Hedvig Lindahl.
"Tonight, the Japanese were a bit more eager to win," Sweden coach Thomas Dennerby said.
Sawa, still a standout in her fifth World Cup, then got redemption in the 59th minute. Lindahl missed a ball in the goalmouth and the 32-year-old Sawa was there to head it home.
The United States beat France 3-1 in Moenchengladbach earlier Wednesday.
Sweden was dealt a huge setback just moments before the match when trusty midfield captain Caroline Seger had to be pulled from the lineup when an old calf injury flared up again.
"It can happen with your team. You have to handle that as a team and we didn't today," Dennerby said.
After Sweden went in front, Japan methodically got back into the game with the short passing combinations that have become its trademark.
Sweden responded by trying to send deep balls to star striker Lotta Schelin, but she often fell into Japan's offsides trap.
It rained all day in Frankfurt, so organizers pulled out the retractable roof and the conditions were perfect by game time.