Marta's penalty came after Formiga was fouled by South Korea's So-hyun Cho inside the box, and she sent the penalty into the lower left corner of the goal for the record score.
Formiga had Brazil's first goal, and the 37-year-old became the oldest player to score in tournament history - doing so in her sixth World Cup.
Brazil plays its second group-stage game against Spain on Saturday, while South Korea faces Costa Rica.
Modric, Marta win Best FIFA player 2018 awards