The 42-year-old Date-Krumm had the most lopsided scoreline of the day, 61 62, in 57 minutes over qualifier Zhang Ling.
"After my first round match I was so tired," said the sixth-seeded Date-Krumm, who was also victorious in doubles alongside Chan Chin-Wei. "So today I was thinking 'I hope I don't break two hours.' And I finished very quickly, which is good for me, because now physically I feel better than yesterday.
"Even when I was leading I didn't feel comfortable. I need to finish. Many matches this year I won the first set, was up in the second and ended up losing the match. I need to concentrate on every point."
Date-Krumm also commented on the WTA's new Challenger Series.
"I think it's a good tournament because in Asia we don't have as many events as Europe or America does," Date-Krumm said. "So we need more middle-sized tournaments like this. If players win the tournaments, they get more than 100 points, so it can have a big effect on the rankings too."
No.3 seed Morita was a 62 62 winner over Paula Kania, and Nara got past Tamarine Tanasugarn, 63 06 64.
The top seed's stand at the maiden WTA $125 event was brief, as Peng Shuai was upended by Zarina Diyas in her opener. The 19-year-old Diyas, who came into this week ranked No.351, never faced a break point in her 62 62 defeat of the World No.40 Peng that took just over an hour.
"Today I served really well," Diyas said. "My serve was a big weapon. It was a really good match for me. I'm happy that I won."
Also winning her opener was another teen, 17-year-old Russian Irina Khromacheva, who overcame three set points from 6-3 down in the first set tie-break of her 76(6) 63 triumph over Alexa Glatch.
"I'm really happy because she just won an ITF tournament," Khromacheva said. "It was a really tough match. She served really well and is an aggressive player. My serve worked really well today, which I'm very happy about. In the tie-break, I stayed positive and that helped me. In the second set, it was a difference of just one break."