The France star struck twice in a thrilling 4-3 last-16 defeat of Argentina to send Les Bleus into the quarter-finals, becoming the first teenager to score more than once in a World Cup game since 1958.
Mbappe became the youngest goalscorer for France at a major tournament when he scored a close-range winner to down Peru in Russia 2018's group stage.
The Paris Saint-Germain forward - the second-most expensive player in history behind team-mate Neymar - went one better as France beat Argentina in Kazan.
The scores were level at 2-2 when Mbappe seized on a loose ball in the box, skipped into space and thumped a low drive through goalkeeper Franco Armani.
Within four minutes Mbappe struck again, racing on to an Olivier Giroud pass to slot a neat finish past Armani to set up a last-eight meeting with either Portugal or Uruguay.
Pele remains the youngest player to have scored at least twice in a World Cup match, the Brazil legend hitting a double against Sweden in the 1958 final at the age of 17.
Although Mbappe is two years older than Pele, the France star has announced himself as a star of the present - as well as the future.