The 2001 U.S. Open champion, Goosen posted a 4-under-par 67 to reach 11-under 202. He's two strokes ahead of Briny Baird and three better than Singh.
A victory would give Goosen a berth in the winners-only Mercedes Championship, the first of two straight PGA Tour events in Hawaii to open the 2004 season. If Singh wins, he clinches the money title.
Goosen is seeking his third PGA Tour win. He claimed his first major crown more than two years ago at Southern Hills in Oklahoma and won the BellSouth Classic last season, earning a berth in the Mercedes both times.
Baird shot a 66, giving him a 54-hole total of 9-under 204. Singh is at 8-under 205 after a 65.