Sun shot a seven-under-par 65 at Jian Lake Blue Bay Golf Club on the southern Chinese island with compatriot Park Sung-Hyun, the new number one, in tied ninth, three shots off the lead.
"Pretty solid overall. I saw a lot of positive things in myself today, so hopefully I can get it going," Sun, who has two wins on the LPGA Tour, told LPGA.com after her lowest round of the season.
Sun leads by one over China's Xiang Sui, who shot a six-under-par 66 with just one bogey, and in tied third was a group of six golfers.
Park Sung-Hyun, the first rookie in LPGA Tour history to earn top spot in the rankings, was at four-under.
"Before I teed off this morning, at the first tee, I received a lot of congratulation texts from friends and family," Park said after her first round as the top player in the world.
"I was a little bit concerned about going into the first round, I thought I might be nervous going through this round.
"But at the first tee, hitting my first shot, I felt comfortable, and the rest of the round was much more comfortable than I anticipated.
"So it was no problem for me."