Les Bleus set up a meeting with Paraguay in Philadelphia on Saturday.
The France captain struck once either side of the interval to take his tally to 10 goals in World Cup knockout matches, making him the competition's most prolific scorer in the elimination rounds.
His brace also lifted him onto six goals at the tournament, leaving him tied with Lionel Messi at the top of the Golden Boot race.
Played in sweltering conditions in New Jersey, France controlled proceedings from the outset but had to wait until the closing moments of the first half to break through.
Mbappe had already seen an effort ruled out for offside, struck the post from Jules Kounde's low delivery, while Michael Olise hit the woodwork with a spectacular scissor kick before Ousmane Dembele fired the rebound wide.
"There's always room for improvement," said France coach Didier Deschamps. "Mainly efficiency, especially in the first half. But between the two posts, the two stops of the goalkeeper, we had a bit of a laborious start.
"A little on the tip of the toes, even if the field doesn't help. But that too, we tend to do a little. Afterwards, when it unfolds and there is the concentration of everyone.
"Yes, of course we have quality to create opportunities, score goals. And not to take it, it's a very good thing too."
Sweden goalkeeper Jacob Widell Zetterstrom produced a string of excellent saves but was finally beaten when Dembele's through ball released Mbappe, who skipped past Viktor Gyokeres with a stepover before finishing confidently.
Sweden almost responded immediately after the restart, only for Elliot Stroud to blaze over from 12 yards. France soon doubled their advantage when Bradley Barcola converted Olise's pass eight minutes into the second half.
Dembele and Olise were both denied by Widell Zetterstrom before Olise created Mbappe's second in the 74th minute. Gyokeres squandered Sweden's best late opportunity, with Mike Maignan making the save.
"The better team won, congratulations to France," said Sweden head coach Graham Potter.
"I thought in terms of the game we had to be perfect and even if we were I'm not sure that would have been enough if I'm brutally honest, because the opponent was of a high level.
"I have no complaints of the players whatsoever. I said to them after the game I don't think it's a disgrace to lose to France, they're a better team and they've got some high-level players."
England will be without two key right-backs for their World Cup last-32 tie against DR Congo on Wednesday after injuries ruled both Jarell Quansah and Reece James out of contention.
England will stick with the penalty shoot-out methods introduced by former manager Gareth Southgate should their FIFA World Cup knockout tie require spot-kicks, coach Thomas Tuchel has confirmed.
Ivory Coast continue their breakthrough 2026 World Cup campaign when they face Norway in a round-of-32 tie at the AT&T Stadium in Arlington, Texas on Tuesday, with both sides arriving from impressive group-stage performances.
Jordan Henderson has called on England to remain focused and disciplined as they enter the knockout stages of the 2026 FIFA World Cup, warning his teammates that there will be no easy matches on the road to glory.
