Bradley Barcola added the second goal in a commanding display that confirmed France as the team to beat in North America. Les Bleus face Paraguay on 4 July in Philadelphia.
Mbappé's first came right on half-time after France had already struck the woodwork twice — once through Mbappé himself and once through Olise's spectacular overhead kick. Ousmane Dembélé and Olise combined at a short corner, finding Mbappé at the byline, and he cut inside Viktor Gyökeres before bending a fierce drive into the far post.
The second arrived eight minutes after the restart. Olise threaded a perfectly weighted ball through Gustaf Lagerbielke's legs for Barcola, who met it first-time and thumped it past Jacob Widell Zetterström.
Olise completed his brace of assists on 74 minutes, sliding another precision pass through for Mbappé, who lifted his effort over the onrushing keeper to wrap up a commanding win.
Mbappé now has six goals at this World Cup, level with Argentina's Lionel Messi at the top of the Golden Boot standings, and 18 in total at the finals — one behind Messi's all-time record of 19. His knockout-stage tally of 10 is the most in World Cup history, breaking the record he shared with Brazilian greats Leonidas and Ronaldo.
Olise's five assists are the most by any player at a single World Cup since Germany's Thomas Hässler in 1994, with only Pelé — who provided six in 1970 — having done better in the era of recorded statistics.
France coach Didier Deschamps, returning to the touchline after missing the final group game against Norway to attend his mother's funeral, was measured in his assessment.
"Until our match, there had been nothing but complicated, very difficult round-of-32 ties. I won't say ours was simple, but we had some margin.
"We could have been more efficient in the first half — that needs to be appreciated. We know we have another one in four days.
"The players are prepared for that, they are here for that. There is another step to take — this one has been taken. It is logical and natural, but it has to be appreciated. When you do things well with a good state of mind, with a lot of pride."
Midfielder Aurélien Tchouaméni cautioned against complacency despite France's firepower.
"It would be a lack of humility — we know what we are capable of as a team. From the moment we make the efforts together and play with our qualities, we can do great things. But there are many steps.
"Our starts to games — we can do a bit better. When we arrive at the beginning of a match, the opponent has a lot of energy. Where we are strong is that we manage to stay calm and we will have our moments. When you look at the attacking potential we have, in the history of football, it is very rare. We take pleasure in watching them play. We try to do everything to put them in the best possible position."