Swedish great Ibrahimovic who now plays in the U.S., challenged the former England captain on Saturday to a wager on the outcome of today's game.
"We've done great up until now, but we look it's another step we've got to overcome".
A long-time favourite of Southgate, his clipped a first-time cross to the back post and Alli had space to head firmly past Olsen in front of the hardy England support.
Dele Alli 8 - A huge moment in Alli's still-young career as he got his first World Cup goal.
- Both of the previous World Cup meetings between Sweden and England have finished level, 1-1 in 2002 and 2-2 in 2006 (both in the group stages).
Southgate feels privileged to "connect everyone through football" and hopes to keep the party going back home. "The fans at home, I'm sure we'll see some videos tonight of them enjoying it".
Alli has also come up the hard way and helped put a frustrating tournament behind him by wrapping things up after team-mate Raheem Sterling wasted chances and Jordan Pickford superbly denied Sweden's Marcus Berg.
Yet to get off the mark at this World Cup, but England should not treat lightly a man who has scored 98 goals in 137 appearances across the past five league seasons for Panathinaikos and Al Ain. "It was a great cross by Jesse and Dele is at his best when he makes those forward runs". "We worked on that in practice".
Janne Andersson's men were the first of these two sides to secure their last-eight spot with a 1-0 win over Switzerland on Tuesday, courtesy of Emil Forsberg's deflected second-half strike.More news: Donald Trump still pondering Supreme Court pick as big reveal nears
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And Nigerians, via Twitter, have congratulated them on their win in Samara.
"Hopefully I carry on scoring and we go far", Kane said.
It took a set play to break the deadlock, as Harry Maguire rose to nod in a corner on the half-hour mark, the eighth out of 10 England goals from dead ball situations.
England dismantled Sweden's tactical defensive game-plan like it was an Ikea wardrobe assembled with the drawers upside down: boredom and frustration leading to patient probing before eventually getting the required pieces in the right positions to successfully complete the job.
"Vardy didn't train today, so is looking doubtful for this game", Southgate said on Thursday. He is likely to retain his starting place for the semifinals.
"You won't find a better team - Sweden are world champions of team spirit".
"He's good - I want to play tomorrow, so...", the striker said with a smile sat alongside the Three Lions boss at the Samara Arena.
"I spoke before the tournament about the togetherness, the trust and that, but we always wanted to prove it on the pitch and show on the pitch that we can do that".