Sorenstam, competing against male players for the first time since the Colonial, made a 6-foot eagle putt on the 504-yard, par-5 second hole for her first $5,000 skin, and took three more skins and $15,000 with a 6-foot birdie putt on the par-3 fifth.
'I'm always nervous,' Sorenstam said. 'That one skin, it felt comfortable to make eagle.'
She had the eagle and four birdies on the front nine of Tanah Merah's Garden course.
'Spectacular golf,' Parnevik said.
Goosen, the 2001 U.S. Open champion, was the only other player to earn a skin, taking $5,000 on the opening hole.
Sorenstam had a chance to add $25,000 to her tally on the par-3 eighth after hitting her tee shot within inches, but Parnevik holed a 10-footer for birdie to halve the hole.
In May, Sorenstam became the first woman in 58 years to play on the PGA Tour when she competed in the Colonial.
Last week in Japan, Sorenstam wrapped up her sixth LPGA Tour player of the year award, winning the Mizuno Classic by nine shots for her sixth victory of the year. She had a 24-under 192 total to break the tour record for a 54-hole event by three strokes.
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