Mbappe became the youngest player to score for Les Bleus at a World Cup when he ran onto Olivier Giroud's deflected shot to tap home into an empty net.
It was another blow for Peru after a strong start had not produced a breakthrough. The South American fans outnumbered the French in stadium and their team has been using any opportunity to pressure France.
Striker Paolo Guerrero had the best chance for Peru in the 31st after collecting a pass from Christian Cueva but France goalkeeper Hugo Lloris saved his low shot from close range.
Still, France appeared to be the more dangerous team as half-time approached Lucas Hernandez had a shot blocked by goalkeeper Pedro Dallese late in the first half. Earlier, Antoine Griezmann and Paul Pogba missed the target.
Peru started the second half in similar fashion to the first, working the ball well into the final third but failing with the all-important final ball.
Pedro Aquino nearly gave the largely Peru support something to cheer when he let fly from fully 35 yards but his shot hit the outside of Lloris' goal and spun wide.
The South Americans continued to push and looked to finally find space in the area as Andre Carillo darted in but his cross was overhit and Jefferson Farfan could only find the side netting.
France risked angering the crowd when Mbappe first took an age to leave the field with still 15 minutes to play before, just minutes later, Giroud was holding up the ball in the corner flag.
It was to be further disappointment for Peru who were, for the second game running, unable to give their huge travelling support a moment to cheer and now face Australia with nothing to play for.
Source: Evening Standard