Nicknamed "my little Obama" by his former Monaco teammate Benjamin Mendy, 19-year-old Mbappe's first-half effort secured a second consecutive win for the French.
Competing in a first World Cup since 1982, Peru's dreams of reaching the last 16 are now over after a second defeat of the tournament.
Though Peru are eliminated, Group C is still set for an intriguing final round of matches as Denmark and Australia, who drew 1-1 in Thursday's first match, are still in contention to join France in the last 16.
Australia, trailing unbeaten Denmark -- currently second in Group C -- by three points will need to beat Peru on June 26 if they are to have any chance of progressing, but following the South Americans' display against France that will be no easy feat.
Peru impress in defeat
Though their World Cup winless run extended to eight matches with defeat against 1998 world champions France, the Peruvians were far from outclassed by one of the tournament favorites.
In an entertaining match, the first half in particular was full of chances. Just 15 minutes had elapsed and Paul Pogba, Raphael Varane and Antoine Greizmann had all gone close for France.
But the best opportunity of the fhalf fell to Peru's returning record goalscorer Paolo Guerrero, who cannily ran across goal but shot directly at Hugo Lloris, making his 100th international appearance, from eight yards.
Guerrero, banned for 14 months by the Court of Arbitration for Sport (CAS) for an alleged drugs violation but cleared to compete in Russia, was left to rue his miss when, shortly after, teenager Mbappe found the net.
The Paris Saint-Germain striker, who was born in the year France won the World Cup, tapped in from a couple of yards after Oliver Giroud's strike deflected off a Peru defender and looped over goalkeeper Pedro Gallese towards the unmarked Mbappe.
Buoyed by their vociferous supporters in the Ekaternburg Arena, Peru went in search of an equalizer -- Pedro Aquino struck the crossbar in the 50th minute with a thunderous 35-yard effort which would have been a contender for goal of the tournament had it gone in.
Andre Carrillo and Luis Advincula both went close with shots from distance but France, despite being on the ropes for long periods, held on.
VAR comes to Australia's rescue
The Video Assistant Referee (VAR)
once again played a starring role at a World Cup
match as Australia secured a 1-1 draw against Denmark courtesy of a controversial first-half penalty.
Mile Jedinak scored his second penalty of the tournament after Yussuf Poulsen was deemed to have handled the ball following an Australian corner.
Although Poulsen's hand did make contact with the ball as he challenged for the ball with Mathew Leckie, it was unclear even after numerous replays whether the Denmark forward had deliberately handled.
But, having initially dismissed Australia's appeals, referee Antonio Mateu pointed to the spot after reviewing the incident.
Within seven minutes Denmark had taken the lead through Eriksen. The Tottenham forward hit his 12-yard effort with such power, it left Australia goalkeeper Matt Ryan with little chance in goal.
But despite conceding early, it was Australia which looked more decisive in possession - with creator-in-chief Leckie particularly impressive -- and it was the Aussies who had more attempts on goal, keeping Denmark goalkeeper Kasper Schmeichel particularly busy after the break.
Their endeavor deserved an equalizer, though the manner in which they scored will spark numerous debates.
The Danes thought they had successfully defended a corner but, with the play having moved to the other end of the pitch, Mateu awarded the penalty following the intervention of the VAR.
Poulsen, who was also the offender when Denmark conceded a penalty to Peru through VAR in their opening match, received a yellow card in the process and will miss Denmark's crucial encounter against France on June 26 as it is his second booking of the tournament.