Shin has won twice this season, including a major triumph at the Women's British Open.
Na Yeon Choi, Eun Hee Ji and Ji Young Oh were tied for fourth at 70.
The 31-player field will be reduced to just 16 after the second round and to eight after the third round.
Sorenstam, who plans to leave the circuit after this tournament, won the event four times before it changed to its current form. This is the third time it has been played in this format and she has missed the weekend each of the last two years.
Sorenstam shot a 74 that left her tied for 23rd.
"I actually thought I played really well today," Sorenstam said. "I just could not put it together."
Ochoa, the defending champion, shot a 75. Both Stanford and Webb had a 73.
Celebrity Families of 2014 [PHOTOS]