Mbappe put France ahead in the 61st minute and then scored the winner in the 86th with his right thigh as Les Bleus became the first team to advance to the next round.
Denmark defender Andreas Christensen equalized for his team with a header in the 68th.
Mbappe scored four goals when France won the World Cup four years ago, including one in the final. He now has 31 goals for France, moving him one ahead of Just Fontaine — the all-time leading scorer at a single World Cup with 13 goals at the 1958 tournament.
France beat Australia 4-1 in its opening game while the Danes drew 0-0 with Tunisia. The Aussies beat Tunisia 1-0 earlier Saturday.