Cook began last week ranked 63rd in the world but jumped 21 spots to No. 42 with his runner-up showing at Muirfield Village.
Monday was the deadline set by the United States Golf Association for players to make the top-50 in the world ranking. Players outside the top-50 who are not already exempt for the U.S. Open will have to earn a spot through next week's 36-hole qualifier.
Cook, 44, grabbed a spot in the British Open as well, as Monday was also the cutoff set by the Royal & Ancient Golf Club of St. Andrews, the governing body of golf's oldest championship.
Cook, who hasn't played in the British Open since missing the cut in 1997, will get to tee it up at Muirfield in Scotland, the site of his second-place finish to Nick Faldo in 1992.
Faldo, on the other hand, will need to play the U.S. Open qualifier if he wants a chance to compete in his 60th consecutive major championship. The 44- year-old Englishman needed a top-two finish at the Volvo PGA Championship this past weekend, but wound up two shots out of second place in the European Tour's flagship event at Wentworth Club.
Faldo, who was 78th in the ranking, moved up to No. 62 after finishing tied for fourth.
Anders Hansen of Denmark made his first career victory a big one with a win at the Volvo PGA, but finished one spot out of the top-50 after vaulting from 141st in the world to 51st.
Charles Howell III dropped from 50th to 53rd and will have to go the qualifying route to make the field at Bethpage. Although the reigning PGA Tour Rookie of the Year recorded three top-10s in his first five starts of 2002, he hasn't finished in the top-15 since February and has missed the cut twice in his last three events.
Tiger Woods, who was seeking his fourth straight win at the Memorial but tied for 22nd in defense of his title, remained firmly entrenched as the top-ranked player in the world, followed by Phil Mickelson, Ernie Els and 2001 U.S. Open champion Retief Goosen.
The recently slumping Sergio Garcia -- two missed cuts and a 73rd-place finish at the Memorial in his last three events -- stayed in the fifth position.
David Duval's tie for fourth at the Memorial marked his first top-10 of the season. The 2001 British Open champion moved up one spot to No. 6 in an exchange of positions with last year's PGA Championship winner David Toms.
Vijay Singh held on to the No. 8 spot.
Furyk climbed 14 spots to No. 9 courtesy of his two-shot win on Sunday. Chris DiMarco, who was idle this week, moved up from 11th to 10th in the world.
Colonial winner Nick Price and Ireland's Padraig Harrington both fell two spots, Price from ninth to 11th and Harrington from 10th to 12th. Davis Love III, Argentina's Angel Cabrera, Rocco Mediate and Northern Ireland's Darren Clarke each slipped one slot to Nos. 13, 14, 15 and 16, respectively.
Although hampered for much of this season with a bad back, Colin Montgomerie has managed to finish in the top-three in his last three starts on the European Tour. The Scot's world ranking improved four places with his move from 21st to No. 17.
Kenny Perry, Canadian lefthander Mike Weir and two-time Masters champion Bernhard Langer of Germany rounded out the top-20.
Spain's Jose Maria Olazabal, another winner of two green jackets at Augusta National, dropped out of the top-20 this week, as did U.S. Ryder Cup captain's pick Scott Verplank. Olazabal fell from 18th to 21st while Verplank slipped from 20th to 23rd.