Les Bleus edged a tense first half leading 2-1 , with Mario Mandzukic putting through his own net and Antoine Griezmann netting a penalty either side of Ivan Perisic's goal.
But with Croatia seeking a way back in the game opened up after the break, and France took full advantage.
Pogba and Mbappe were on target in quick succession with fine long-range efforts past Daniel Subasic, and in doing so each player made their little bit of history.
Mbappe, 19, became the first teenager since Pele to score in a World Cup final with his strike.
19y 207d - Kylian Mbappé is the 2nd youngest player to score in a @FIFAWorldCup final, after Pelé (17y 249d) in 1958 for Brazil. Anointed. #WorldCupFinal #WorldCup #FRA #CRO pic.twitter.com/RAX9fOPWL0— OptaJoe (@OptaJoe) 15 de julio de 2018
Sixty years had come and gone without anyone matching the legend's record, until the PSG wonderkid decided to strike.
Pogba, too, set an historic first for his employers, Manchester United.
Never before had a United player scored in a World Cup final prior to Pogba's crisp effort in the second half to extend the lead against Croatia.