Japan played tough defense after New Zealand's Amber Hearn scored an equalizing goal in the 12th minute. The Kiwis didn't get another chance from then on as the teams remained deadlocked at 1-1 through much of the game.
Japan finally took advantage when Miyama nailed down three vital points with her well-taken free kick. Mana Iwabuchi set up the play when she drew a foul near the edge of the penalty area that allowed Miyama to curl in the winning tally.
Yuki Nagasato had given Japan a quick 1-0 lead in the 6th minute.
Japan will next play Friday against Mexico and the Kiwis, still looking for their first World Cup win, will take on England the same day.