Far more fancied England sides had failed to reach the last four in the past but Gareth Southgate's young squad powered on as they continued to make a mockery of dampened pre-tournament expectations with another impressive display in Russia.
They were set on their way when Maguire rose imperiously to head home from a corner and Alli added the killer blow after the break as England showed they are not entirely dependent on the tournament's leading scorer Harry Kane for goals.
If anything, England's hero on the day was to be found at the other end of the pitch as keeper Jordan Pickford produced three superb saves to shut out the workmanlike Swedes.
"We had to withstand a lot of physical pressure," said England coach Gareth Southgate. "The resilience of the team and togetherness of the team today was crucial. Today our spirit was as good as theirs and our quality a little bit better."
The fans who serenaded their side at the Samara Arena stayed long after fulltime to herald the achievement, knowing that with so many of the favourites having departed, England have arguably their best chance of global glory in more than half a century.
Hosts Russia or Croatia, who meet later on Saturday and are lower ranked than Southgate's side, are all that stands between England and a first World Cup final since they won the tournament on home soil in 1966.
Yet while England's victory, only their third quarter-final success in nine attempts, was largely a one-sided affair it was certainly not straightforward.
Sweden had reached the quarter-finals by making life hard for supposedly superior opposition and it was easy to see why after a dour opening when England looked incapable of stringing passes together against their hardworking opponents.
It was predictable in many ways, therefore, that the deadlock was broken from a set piece.
BULLET HEADER
England had laboured without reward before Ashley Young lined up a corner on the left and his curled effort was met by Maguire charging forward with conviction and barging Emil Forsberg out of his way to power a header down into the net.
That was England's eighth set-piece goal at this World Cup, but, while they are lethal from dead balls, apart from Kane they are not blessed with too many other sharp shooters.
Forward Raheem Sterling has faced some criticism over his struggles to score for England and just before halftime his doubters were handed ammunition when he was twice left alone to bear down on Sweden keeper Robin Olsen.
His blushes were saved by the linesman's flag as he fluffed the first chance, but moments later he ran through again, this time trying to round the keeper, only to be denied once more.
England were almost made to pay straight after the interval and would have been pegged back if Pickford had not produced a top-drawer save to keep out a Marcus Berg header.
The importance of the keeper's contribution was swiftly underlined with England doubling their lead in the 59th minute as Jesse Lingard's teasing cross into the box was met by Alli unmarked at the far post to head powerfully past Olsen.
England had not kept a clean sheet in their four previous matches and had Pickford to thank for ensuring they did not concede this time.
He saved superbly from Viktor Claesson before tipping a shot from Berg over the bar and that was enough to ensure Swedish hopes of reaching their first semi-final since 1994 were dashed.
"I wasn't born the last time England reached a World Cup semi-final," said Pickford. "We have always said we would take one game at a time and we can go on and create our own history."
(Reporting by Toby Davis; Editing by Ken Ferris)
