They will now face either Croatia or Russian Federation, who play later on Saturday, and Andersson said the Three Lions can go the distance.
Swedish players applaud their fans after their loss to England.
The third-place game, between the semifinals losers, will be played on Saturday, July 14.
The former Manchester United star wrote on social media: "If England win I buy you dinner wherever you want in the world, but if Sweden wins you buy me whatever I want from Ikea, okay?"More news: Defending Champion Garbine Muguruza Knocked Out In Wimbledon 2nd Round
Maguire epitomises the graft this squad have put in over the years and headed home his first global goal after 30 minutes, continuing his rapid ascent from fan in France at Euro 2016 to England hero in Russian Federation.
England goalkeeper Jordan Pickford made several crucial saves throughout the match to record the Three Lions' first clean sheet at Russian Federation 2018.
Thankfully for Southgate's men, they are a dab hand at set pieces and their first corner brought the opening goal.
He told the BBC: "I'm really pleased for Dele (Alli)". He is best at making those runs for the goal and he can finish. With the match coinciding on a weekend, a time specially opted by those tying a knot on a Saturday, many British fans took to Twitter to share how they tried to strike a balance - match and a wedding.More news: England fans 'dare to dream' after win over Sweden
Then, as Sweden looked to get back into the match, the favorites finished them off.
They began solidly against England in a slow and sloppy start to the game that resembled a pre-season friendly at times, only to be outdone by a goal Sweden isn't used to conceding.
If England do beat Sweden and reach the last four, their next match will be in Moscow on Wednesday night, which will be far more accessible. Sterling got hold of the loose ball but his shot was deflected over.
There was emotional scenes in Russian Federation and at home among the England fans, who have long suffered from tournament heartbreak. "You have to respect you are faced with a good keeper", Andersson said.More news: Suzuki details all-new, SA-bound Jimny mini-4x4