Date-Krumm, who was ranked in the world's top 10 when her opponent was born in 1994, was utterly ruthless in exploiting Robson's poor serving on her way to a 6-4 6-4 victory.
The British star, seeded seventh for the event, got just 58% of her first serves in, and with Date-Krumm winning 18 of the 27 points played on Robson's second serve she was able to earn 10 break points, of which she converted four.
Robson tried hard to cling on despite her serving problems, and earned seven break points of her own - but Date-Krumm held her nerve to save all but two of them, coming through the match to the delight of the crowd and earning a second round match against fellow Japanese Misaki Doi.
Italian fourth seed Flavia Pennetta also crashed out, losing 3-6 7-5 6-0 to American Vania King despite battling away to save 17 of the 23 break points King earned during the match.
Wimbledon finalist and second seed Sabine Lisicki came through her opening match against South Africa's Chanelle Scheepers 7-5 7-6(1), while sixth seed Madison Keys beat qualifier Anna Scmiedlova 6-3 6-2.
Japan Open, Osaka - First round results on Tuesday
2-Sabine Lisicki (Germany) beat Chanelle Scheepers (South Africa) 7-5 7-6(1)
Vania King (U.S.) beat 4-Flavia Pennetta (Italy) 3-6 7-5 6-0
6-Madison Keys (U.S.) beat Anna Karolina Schmiedlova (Slovakia) 6-3 6-2
Kimiko Date-Krumm (Japan) beat 7-Laura Robson (Great Britain) 6-4 6-4
9-Kristina Mladenovic (France) beat Aleksandra Wozniak (Canada) 7-6(4) 6-4
Barbora Zahlavova Strycova (Czech Republic) beat Hsieh Su-Wei (Taiwan) 6-2 6-2
Polona Hercog (Slovenia) beat Petra Cetkovska (Czech Republic) 6-4 5-7 6-1
Zheng Jie (China) beat Sharon Fichman (Canada) 6-2 6-1
Belinda Bencic (Switzerland) beat Lauren Davis (U.S.) 6-3 7-5
Luksika Kumkhum (Thailand) beat Ayumi Morita (Japan) 6-2 6-1
Zhang Shuai (China) beat Anabel Medina Garrigues (Spain) 6-0 6-3