Sofia Jakobsson could have put the Swedes ahead after just 30 seconds, while Stina Blackstenius also hit the bar early on.
And they then fell behind after 34 minutes when Beth Mead smashed home from inside the box, before second-half goals from Lucy Bronze, Alessia Russo and Fran Kirby finished things off.
It means that it will be England who will play either Germany or France at Wembley Stadium on Sunday as they bid to win their first European Championship, after losing in the final in 1984 and 2009.
Chelsea defender Magdalena Eriksson was frustrated after the game, telling reporters: "I'm very disappointed of course, there's a lot of emotions at the moment.
"An extreme disappointment, it's a tough one to take because we started the game extremely well. We could have been one or two nil up after 20 minutes.
"When you don't score, you don't take your chances, when you don't score when you have momentum, it's tough.
"The timings of their first two goals are really crucial. It just became too much of a challenge when it was 2-0."
Sweden, ranked second in the world by FIFA, have quietly come through the rounds to reach the last-four stage.
They beat Belgium 1-0 in Friday night's quarter-final at Leigh, with near-relentless pressure paying off in stoppage time when Linda Sembrant finally found the net.
Eriksson, who captains Chelsea in the Women's Super League, is set to face club-mates including Fran Kirby and Millie Bright in Tuesday's Bramall Lane semi-final clash.
England have reached the final four for a second consecutive Women's European Championship, and they lost 3-0 to the Netherlands last time.
This time the Lionesses are riding the wave of popular support in England, with a huge audience of 9.1million tuning in on television and online to watch the 2-1 quarter-final win over Spain.
Quoted in Swedish newspaper Expressen after Friday night's game, Eriksson said she was relishing the prospect of tackling Sarina Wiegman's team at the home of Sheffield United.
"It is incredibly special. I was happy when they progressed, it will be an incredibly cool challenge," Eriksson said.
"We want to do everything we can to ruin their party. They have done well and I know a lot of their players."
Match-winner Sembrant said it felt "absolutely magical" to get over the line against Belgium and tee up the England clash.
"It will be a hugely exciting match to meet them in England in a semi-final," Sembrant said. "It will be really cool. Now we have to recover and recharge."
