Montgomerie finished with nine skins worth $75,000 while Woods had five skins totaling $51,000. South Korea's K.J. Choi also collected $51,000. South Korea's Se Ri Pak, the only woman competing, missed several chances and ended with no skins.
Montgomerie took the lead with a 12-foot putt on the par-4 first hole at Raon Golf Club on the island of Jeju. The Scotsman, a member of Europe's Ryder Cup-winning team, sank a 30-foot birdie putt on the par-5 10th to collect five skins.
Woods took the second hole and earned a total of five skins with a birdie putt on the 12th and another at the 14th.
Sunday's prize money goes to charity.
Woods, making his first visit to South Korea, expressed confidence Friday that his new swing will pay off. He drew criticism this year for changing a swing that helped him become golf's dominant player. This year, he lost his top ranking to Vijay Singh and his only victory came at the Match Play Championship in February.
Woods will travel to Japan for next week's Dunlop Phoenix tournament.
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