Japan's Morimoto converted a last-minute penalty stroke to spoil India's party in the second outing of the four-match International Friendship Hockey Series in Tenri, Japan, on Thursday.
Thee late goal enabled the Japanese snatch a 1-1 draw.
Jasjeet Kaur Handa scored from a penalty-corner to give India the lead in the 20th minute.
The Indians maintained the lead till the last minute, but Japan won a penalty-stroke in the 70th minute and drew parity from it through Morimoto.
India lost the opening match 1-2 on Tuesday.
Japan's Kaori Chiba scored a brace to put the visitors in command before the lemon break. She converted a penalty-corner in the second minute and then scored a field goal just before half-time.
India pulled a goal back in the 48th minute through Surinder Kaur.
The next match of the series will be played on Saturday.
The Mamta Kharab-led Indian team had earlier beaten Nanto Bank 3-0 in its opening warm-up game, and got the better of Tenri University 3-1.
In the match against Nanto, Mamta, Surinder Kaur and Saba Anjum scored.
The Indians staged a fightback to win the second game. Rattan Summer put Tenri ahead by converting a penalty-corner, But, Suman, Saba and Mamta scored to ensure the visitors victory.
