Hamilton, who defeated 2002 British Open winner Ernie Els in a playoff, came in 16th this week. Hamilton became the second straight rookie to hoist the claret jug after Ben Curtis won last year.
Tiger Woods tied for ninth place at Royal Troon and is atop the rankings for the 258th consecutive week. The race has tightened as Els is now less than one point from claiming the top spot.
Vijay Singh came in third this week, while Phil Mickelson, who finished third at the British Open, stayed in fourth. Davis Love III rounded out the top- five.
Retief Goosen, the reigning U.S. Open champion, stayed in sixth, followed by Mike Weir, Padraig Harrington, Jim Furyk and Sergio Garcia.
Adam Scott, Kenny Perry and Chad Campbell remained in spots 11-13. Darren Clarke and Stuart Appleby switched places from last week with Clarke moving up to 14 and the Australian falling to 15th.
Hamilton took 16th, while David Toms fell one to No. 17. Scott Verplank climbed one rung to 18th, but Stephen Ames and Fred Couples each fell two spots to complete the top-20.
Jonathan Byrd won the B.C. Open in New York and vaulted up 24 places to No. 79. The win was his second on the PGA Tour after titling at the 2002 Buick Challenge.