Goalkeeper Jordan Pickford then produced a series of crucial saves in the final half-hour to seal England's long-awaited spot in the last four.
"Yes I definitely believe England are good enough to win the World Cup", he revealed. "They are forceful and well organised".
This was England's most complete performance of Russian Federation 2018 in what was a highly-credible team effort.
"To be in charge of a group of people who give as much energy and give me as much as they have over this period of time, committed to so much, is very special".
"I was going to say if we go two penalty kicks we'll be fine, but I can't say that anymore can we", one Swedish fan said.
Alli, who turned 22 in April, nodded home Jesse Lingard's second-half cross to help England to a 2-0 quarter-final victory in Samara on Saturday, locking down a semi-final meeting with Croatia in the process.
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"They have nine players who are playing in the English Premier League so there'll be something of a British accent". Giroud has played 380 minutes of France's 2018 World Cup campaign, but is yet to score. "I'm not jealous.
They'll now play Croatia, who won their quarter final by knocking out hosts Russian Federation on penalties.
"Personally, I don't think I played as well as I should have", he said.
"It's great to see all of the players sat with their families out there because they feel like they've been part of this in the last few weeks as well". "To get through the two games this week we needed all of that". "The resilience of the team and togetherness of the team today was crucial".
The 1966 World Cup champions last reached the semifinals in 1990, losing the first of a series of haunting penalty shootouts.
Fabian Delph 6 - On for Alli late in the game, Delph made sure England continue to tick over in possession and resisted any comeback from Sweden.
Sweden needed a change in approach and immediately after the restart, they nearly found an equaliser when a cross was delivered for Marcus Berg at the back post, but the forward's header was superbly kept out by the left hand of Pickford.