New Zealand took a 1-0 lead in the Group A match on an own-goal by Ayu Nakada in the 11th minute and doubled the advantage four minutes later on a long-range effort by Rosie White.
Tanaka cut the lead in the 37th and Michigami's header in the 71st pulled the hosts level.
Both Japan and New Zealand have four points. Japan next faces Switzerland while New Zealand takes on Mexico on Sunday.
Also in Group A, Sofia Huerta and Olivia Jimenez scored in the second half to lead Mexico to a 2-0 win over Switzerland for its first win of the tournament.
Switzerland was handed its second loss and cannot advance to the quarterfinals.
In Saitama, Giovanna Oliveira's header in the 87th minute gave Brazil a 1-1 draw with Nigeria in Group B.
Francisca Ordega gave Nigeria a 1-0 lead with a superbly hit drive in the final minute of the first half but Oliveira's late equalizer secured a share of the points for Brazil.
Nigeria has four points and plays Italy on Sunday. Brazil, with two points, faces a must-win encounter with South Korea.
South Korea beat Italy 2-0 on second-half goals from Lee Geum-min and Jeoun Eun-ha.