Simpson had four birdies in a five-hole span and closed with eight consecutive pars Sunday in winning his first major tournament championship. His final round 2-under-par 68 gave him a 72-hole score of 1-over 281. Graeme McDowell and Michael Thompson tied for second one stroke back.
Simpson moves from 14th to No. 5 in the world rankings following a tournament in which four of last week's Top 10 didn't make the 36-hole cut and only two others -- Jason Dufner and Lee Westwood -- finished in the Top 10.
Both world No. 1 Luke Donald and second-ranked Rory McIlroy, the tournament defending champion, missed Friday's cut. Donald, however, keeps the top ranking with a rankings points average of 10.124. McIlroy is second at 8.864.
Westwood, who tied for 10th at the Open, remains third with 8.283 and Tiger Woods, who was among those in 21st place Sunday, is fourth at 6.783.
Simpson's average is 6.658 while Bubba Watson, another who missed the cut, slips from fifth to No. 6 at 5.992. Matt Kuchar (5.862) is also down on spot to seventh.
Dustin Johnson, who was 10th a week ago, missed the U.S. Open cut and drops to 14th.
This week's European Tour title, won at the Saint-Omer Open in France, went to Darren Fichardt. It was his third European Tour win but first since March 2003 and boosts his world ranking from 307th to No. 179.