Arimura, ranked 19th in the world, made six birdies and an eagle and overcame bogeys on two of her first three holes to post a 10-under 134 total.
“I had a rough start but I controlled myself so it got better in the end,” said Arimura, who has never won outside of Japan. “Whenever I had doubt during today’s play, I reminded myself I should be confident.”
Webb also shot 66 with an eagle on the par-5 ninth.
“I putted really well today,” said Webb, ranked 13th. “It’s nice to see the putts go in and I’m playing solidly.”
Sun Young Yoo of South Korea was four shots back, while countrywoman Na Yeon Choi and England’s Karen Stupples were at 4 under, six shots behind Arimura.
American Cristie Kerr shot 67 to jump to 3 under for the tournament, and countrywoman Michelle Wie was 1 under after a 71.
World No. 1 Yani Tseng of Taiwan, who came to Singapore having won tournaments in each of the last three weeks, shot 72 to put her at 2 under.
“It was a bit of a tough day today, I just couldn’t hit a shot,” Tseng said. “My irons were terrible today. It’s a little frustrating, but 8 behind is not so bad.”