England promptly cranked up the pressure and pulled further ahead on 59 minutes when a completely unmarked Alli sent a thumping header past Olsen after a first-time cross by Jesse Lingard.
Sweden manager Janne Andersson had warned his side England were a match for them at set-pieces, and so it proved when Maguire connected with Ashley Young's corner after a low-key first half hour.
Instead they were nearly pegged back two minutes after the interval from Sweden's first moment of real danger, with Jordan Pickford making a brilliant one-handed save from Marcus Berg.
The Swedes were staying in the five-star Lotte hotel, Samara, on the eve of the World Cup quarter-final.
One of the players, reports Daily Mail, was overheard saying: "We could do without this today".
The standard of England's crossing has particularly stood out this tournament, and another brilliant delivery led to the second goal.
Sweden had reached the quarter-finals by making life hard for supposedly superior opponents and it was easy to see why after a dour opening when England looked incapable of stringing passes together against their hardworking opponents.
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England's appearance in a first World Cup semi-final since 1990 is an "incredible feeling", says boss Gareth Southgate.
The star on the day was arguably Pickford, who is in line to join the excellent Maguire in emerging from this tournament with significantly higher stock. Concern will be minimal, but should England meet Belgium or France in the final, they may need their attackers to click in a manner they have not yet suggested.
England's deep run also is a surprise.
The huge frustration for Sweden will be that they were beaten at their own game. But they were undone from the first corner they had to defend, while failing to make similar inroads at the other end, and it added up to a picture in which their limitations were brutally exposed.
"It might do England a favour though if they are a bit exhausted when they kick off on the match later".
Maguire and Alli struck either side of the interval in Samara.
"We knew we would have the majority of the ball and it was a case of breaking them down because Sweden are a really well organised team".
"We have always said we would take one game at a time and we can go on and create our own history". Here they were too cautious until the game started getting away from them and were punished for uncharacteristic mistakes.