The 32-year-old South African's overtime triumph managed to wipe away a disastrous three-putt from 15 feet at the 18th hole in Sunday's fourth round. Goosen missed the second putt in the sequence -- a mere two-footer -- that would have given him the win in regulation.
However, Goosen dominated the playoff with timely birdies and a number of gutsy up-and-downs to open a five-shot advantage. Brooks cut Goosen's lead to three after a two-shot swing at the 17th, but Goosen needed only to bogey the last hole to secure his first win in the U.S. and his first in a major championship.
Top-ranked Tiger Woods, who finished a surprising 12th in defense of his 2000 U.S. Open title, still holds a big lead over No. 2 Phil Mickelson. Woods came up short in his quest for a record fifth straight major title, while Mickelson continued his streak of major disappointments.
The lefthander, just two shots off the pace heading into Sunday's round at Tulsa's Southern Hills, carded five birdies over the final 10 holes to blow up to a 75. He tied for seventh, six shots back of Goosen and Brooks, for his 13th top-10 finish in a major.
Mickelson will get his next shot in one month at the British Open at Royal Lytham and St. Annes, where he tied for 41st in 1996. He has never finished in the top-10 at a British Open; his best showing was a share of 11th place last year at the Old Course at St. Andrews.
Ernie Els, a South African who also captured his first title on U.S. soil in a playoff at a U.S. Open, remained in third place, followed by Fiji's Vijay Singh and England's Lee Westwood.
Els defeated Loren Roberts and Scotland's Colin Montgomerie in the extra session at sweltering Oakmont in 1994. He also went on to win the 1997 U.S. Open at Congressional.
Davis Love III moved up one spot to No. 6 in an exchange of positions with David Duval. Spain's Sergio Garcia stayed in eighth, while Montgomerie and Hal Sutton rounded out the top-10 in the rankings.
Canadian Mike Weir climbed one place to 11th. Darren Clarke of Northern Ireland also made a one-spot move up to 12th, followed by Tom Lehman, who was 11th last week.
The next five players held their positions from last week. The unique-swinging Jim Furyk stands in 14th, followed by Michael Campbell of New Zealand, Denmark's Thomas Bjorn, Zimbabwe's Nick Price and the 18th-ranked David Toms.
Angel Cabrera of Argentina moved up from 22nd to 19th on the strength of his tie for seventh at Southern Hills. It marked his best finish in just two appearances in the U.S. Open. He tied for 37th at Pebble Beach last year.
Colorful Swede Jesper Parnevik dropped one spot to 20th, while Paul Azinger climbed two spots to 21st after tying for fifth in Tulsa. Mark Calcavecchia and Ireland's Padraig Harrington are 22nd and 23rd, respectively.
Stewart Cink, who finished solo third at the Open, stayed in 24th place. Cink had a chance to make it a three-way playoff on Monday, but missed a gimme putt of his own on the 18th green Sunday.
Rocco Mediate moved up three places to 25thin the world. Only one shot back heading into the final day of the season's second major, Mediate struggled to a two-over 72 and finished alone in fourth.
Runner-up Brooks, who hadn't notched a top-five finish since winning the 1996 PGA Championship in extra holes, vaulted 101 spots, from 195th to 94th.
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