Rosales, who started the round just one shot adrift of Wendy Ward, Nicole Perrot, Karine Icher and Han with a fiery 5-under par 66 in the opener of the $1.3 million championship, struggled on the soggy fairways and unpredictable putting surface of the par-71 layout.
After a birdie on the par-3 No. 4, Rosales fumbled with a bogey on the par-5 No. 9 but came up with a birdie on the next before coming up with a slew of pars to preserve a 37-33 card for a 70 and a 36-hole aggregate of 136.
Han followed up her 65 with a 68 to seize the provisional solo lead at 133.
"I hope she sustains her fine form and play hurt-free in the final round," said Rosales’ swing guru Bong Lopez.
The second round of the 54-hole tournament was actually suspended due to darkness with 72 players left on the course, including contenders Catriona Matthew (-7 after 8 holes), Icher (-7 after 7 holes) and Michele Redman, Natalie Gulbis and Ward (-6 after 9 holes).
After slow play and darkness forced the first round to be completed on Saturday morning, another delay struck as fog halted play for more than three and a half hours.
That meant 72 players were left to complete their second round in the tournament on Sunday.
Fog was in the forecast Sunday, which could lead to a Monday finish at the Donald Trump-designed course that overlooks the Pacific Ocean south of Los Angeles.
Han was one of the fortunate ones to complete her second round. She followed a bogey-free first round with another consistent showing, moving to nine-under 133.
"We were just waiting, waiting, waiting. It was a little bit frustrating," said Han, who had five birdies and two bogeys. "We finished today, which is a pretty good thing."
The 2001 LPGA Rookie of the Year, Han has been close to breaking through this year with seven top-10 finishes in 21 events.
She has three career wins on the US tour, with the last coming at the 2004 Safeway Classic.
Han is two shots in front of Scotland’s Catriona Matthew and France’s Karine Icher, both of whom were stranded on the course when darkness fell.
Matthew played eight holes at 5-under, while Icher was 1-under through seven.
Seven golfers were three shots back, including tour starlet Natalie Gulbis, who was 1-under through seven holes.
Others in that pack are Tina Barrett, Michelle Redman, Wendy Ward, Chile’s Nicole Perrot and British Open champion Jeong Jang of South Korea and Rosales.
Only Barrett (66) and Rosales (70) completed their second rounds.
"We sat in the clubhouse and watched the fog roll out and roll back in," Barrett said. "They kept telling us every 15 minutes. I think the hardest part was trying to figure out what time we actually were going."
Two-time defending champion Annika Sorenstam signed for a 70 for a three-under total of 139.
"I thought yesterday was a long day, one of the longest days on the golf course," said Sorenstam, who opened the second round with an eagle at the par-4 first hole. — With AFP report