Woods seems to perform best when surrounded by golf's legends. He won Arnold Palmer's tournament earlier this year and accepted the champion's trophy at the Memorial from tournament host Jack Nicklaus.
Woods has won the Memorial five times and Palmer's event seven times. Woods' latest win featured three birdies on the last four holes, including a spectacular chip-in on the 16th.
It was the 73rd PGA victory for Woods, who is tied with Nicklaus for second-most all time. Sam Snead tops the list with 82 wins over 30 years. Nicklaus' 73 wins came over 25 years. Woods is in his 17th year on the tour.
The No. 4 world ranking is the highest for Woods since Feb. 20, 2011. His move from ninth last week forces five golfers down one place each. Martin Kaymer re-enters the Top 10 at No. 10, switching places with 11th-ranked Steve Stricker.
Luke Donald is No. 1, having held the position for a total of 47 weeks, which is sixth most (Woods owns the record at 623 weeks). Donald has an average points ranking of 10.434 with Rory McIlroy (9.057) in second and Lee Westwood (7.915) remaining third.
Woods has an average of 6.785, coming in ahead of Bubba Watson, who is fifth with an average of 6.163, and Matt Kuchar, whose average of 5.948 has him sixth this week. Justin Rose (5.749) is seventh ahead of Hunter Mahan (5.487) and Jason Dufner (5.249).
Kaymer has a ranking points average of 5.037, edging the 5.009 mark of Stricker.
Jaidee Thongchai won the European Tour's Wales Open and improved his ranking from No. 199 to 114th.