After surviving an early period in which Sweden could have easily been out of sight, Sarina Wiegman's side struck through Beth Mead, Lucy Bronze, Alessia Russo and Fran Kirby to humble the Scandinavian powerhouses.
Fans at Bramall Lane were still taking their seats when Sweden were presented with an opportunity to break the deadlock within the first 30 seconds, but the boot of Mary Earps denied Sofia Jakobsson.
It came as little surprise to see the first England chance fall the way of Mead only moments later, as she met the cross of Arsenal teammate Leah Williamson but could not get the desired connection on her header.
A frenetic opening 10 minutes also saw Sweden's Stina Blackstenius head against the bar from a corner, but England survived the early wave of pressure and began to make inroads in Sweden's half as the first period went on.
From potentially finding themselves two or three nil down, England ultimately drew first blood in Sheffield, as Bronze picked up the ball on the right-hand side before finding Mead, who took a touch before swivelling and firing a half volley into the far corner.
The Lionesses got to half time with their slender lead intact thanks to the record-equalling Mead, who matched Inka Grings's record of six goals in a single Women's European Championships with her well-executed opener.
In a strikingly different start to the second half, England took the game by the scruff of the neck and were 2-0 up by the 49th minute, as Bronze headed home in acres of space before the Lionesses faithful were made to wait for VAR to confirm the goal, with Lauren Hemp managing to stay onside in front of Hedvig Lindahl.
The introduction of super sub Russo almost paid dividends within seconds, as the Manchester United attacker powered down the right-hand side in the 57th minute before playing an inviting ball to Hemp, who could only direct the ball onto the crossbar from a yard out.
Sweden refused to wave the white flag, but Earps continued to act as an impenetrable wall in between the sticks and spectacularly tipped a looping Blackstenius effort over the bar with 65 minutes gone.
Just when Earps produced a picture-perfect moment at the other end of the pitch, Russo channelled her inner Thierry Henry with a scintillating backheel through the legs of Lindahl to make it 3-0, just seconds after seeing a point-blank effort saved by the Sweden goalkeeper.
If Lindahl had not already experienced enough ill fortune at Bramall Lane, the 39-year-old then flapped at a long-range Kirby effort and could not race back to her line in time before the ball trickled into the back of the net for England's fourth in the 76th minute.
Russo was inches away from adding a second for herself in the dying embers, as the Lionesses shut up shop at the back to advance to their first major tournament final since 2009.
Either Germany or France will lock horns with England for the chance to be crowned European Champions, with the final taking place at Wembley on Sunday evening.