The 18-year-old Song finished at 10-under 206, one stroke ahead of Sorenstam, who shot a 71.
Sorenstam, younger sister of Annika Sorenstam, traded first place with Song throughout the day after trailing by five strokes entering the final round. The South Korean finally birdied the par-4 370-yard 18th hole to avoid a playoff.
'I wasn't thinking about winning,' Song said. 'There's so many ways you can lose this tournament. For example, if I hadn't made that birdie putt, who knows what would happen?'
After shooting a 65 Thursday and a 66 Friday, Song struggled in the third round.
'You can't really play well all three days,' she said. 'I had a great first and second round, but as expected, I had difficulty with my shots today.'
England's Laura Davies (70) and New Zealand's Lynnette Brooky (70) tied for third place at 208.