Harry Maguire and Dele Alli scored the crucial goals for The Three Lions as they reached the last four of sport’s biggest event for just the third time.
England goalkeeper Jordan Pickford also played a key role, making a string of excellent saves to earn his first clean sheet of the tournament.
Gareth Southgate’s side will now play Croatia on Thursday morning (AEST) for a spot in the decider.
Croatia beat host nation Russia 4-3 on penalties in Sochi after the sides were locked at 2-2 after 120 minutes.
In Samara, after both nations started sluggishly, England took the lead just before the half-hour mark when Maguire rose above Emil Forsberg to score a thumping header from Ashley Young’s corner.
The goal – England’s fourth from a corner at the World Cup – failed to produce much of a response from Sweden before the break.
But Marcus Berg forced a great save from Pickford with a near-post header just after play resumed and that shook England enough to lead to a second goal.
Jesse Lingard provided it, crossing sharply to the back post where Alli was on hand to nod home in the 59th minute.
Sweden had to throw bodies forward from there but struggled to create clear-cut chances, and, when they did, man-of-the-match Pickford was too good, denying Viktor Claesson and then Marcus Berg with smart saves.
It led to a painless finish for the victors, sparking delirious scenes of celebration both in Russia and all over England.
England captain Harry Kane said he and his teammates would not be getting carried away despite being just one match away from a final appearance.
“We know there’s still a big game ahead, obviously the semi-final,” he said.
“But we’re feeling good. We’re feeling confident. Today was great. We looked composed, it looked like we controlled the game. So we just have to go again.
“We’re enjoying it. I know the fans here are enjoying it. The fans back home, I’m sure we will see some videos tonight of them enjoying it, so we’ve just got to keep doing what we’re doing and make the country proud.
“I thought we was fantastic today. It was a difficult game. Sweden have made it tough … we’re buzzing.”
Asked if football was ‘coming home’, a reference to a 1990s song called ‘Three Lions’ that has surged in popularity in England over the past week, Maguire kept his cards close to his chest.
“Hopefully. Fingers crossed,” he said.
Russia’s dream run ends
After a brilliant run to the last eight that included a famous win over Spain, Russia were knocked out of the World Cup in heartbreaking circumstances.
In an exciting contest, Russia forced penalties when Mario Fernandes headed in a dramatic 115th-minute equaliser.
Denis Cheryshev’s wonderstrike in the 31st minute gave Russia the lead but Andrej Kramaric produced a quick response for the victors.
Croatia should have won it in normal time but were denied by the woodwork in the second half, leading to extra time, where Fernandes cancelled out Domagoj Vida’s effort.
A tense penalty shootout followed, with Fedor Smolov and Fernandes missing attempts for the hosts.
Those efforts – and a little bit of luck on Luka Modric’s kick, which went in off Russia goalkeeper Igor Akinfeev and the post – helped set the scene for Ivan Rakitic to score the decisive penalty.
And he made no mistake, sending Croatia to the semi-finals for the first time since 1998.