Woods, 43, never trailed in the match at Royal Melbourne, building a 3-up lead through 15 holes and then closing it out with a 20-footer for birdie at the 16th hole to dispatch the rookie from the International team who was 3-0-1 entering the match.
As the ball approached the hole, Woods took off his cap and made his way to congratulate Ancer.
"Well, when it was probably like 6 feet out -- the match was over," Woods said. "I might have taken the hat off a little early, but it was over.''
The United States had lost the competition just once in 12 previous events, at Royal Melbourne in 1998, when Woods was just 21 and Jack Nicklaus was the captain.
The first playing captain since Hale Irwin held the dual role at the inaugural Presidents Cup in 1994, Woods improved his personal record to 27-15-1 and passed Phil Mickelson as the most successful player in the competition's history.
"I love playing with my teammates, and I couldn't have had a better group of guys to be the captain for,'' Woods said. "It's been a special experience.''
Woods made seven birdies and three bogeys in the 16 holes he played, and now he has two perfect records in nine Presidents Cup appearances. He was 5-0 at the 2009 event.
For the week, Woods went 3-0, winning in four-ball and foursomes on Thursday and Friday. After sitting out Saturday's double session, he came back with the singles win, and now he is 7-2 in that format.