The Irishman earned his first victory of 2002 in a playoff over Eduardo Romero. The win was the fifth of his career on the European Tour.
Charles Howell III also climbed after his first career victory on the PGA Tour at the Michelob Championship at Kingsmill. Howell became the 14th first-time winner on the PGA Tour this season and moved up 21 spots to 39th in this week's rankings.
Tiger Woods remained firmly planted atop the rankings while Phil Mickelson held on to second place.
Ernie Els, the 2002 British Open champion, withdrew from the Dunhill Links Championship Sunday morning as his wife gave birth to their second child. The South African stayed put in third place, followed by fellow countryman Retief Goosen, Spain's Sergio Garcia and Harrington.
David Toms, who was unable to defend his title at the Michelob Championship, dropped one spot to seventh. Vijay Singh remained in eighth, while Davis Love III dropped two places to ninth. Jim Furyk rounded out the top 10.
Nick Price and David Duval stayed in the 11th and 12th spaces, respectively. Colin Montgomerie, who fired a final-round 63 to move into a tie for third at the Dunhill Links Championship, climbed four spots to 13th.
Chris DiMarco came in at 14th this week, followed by Bob Estes and Justin Leonard.
Michael Campbell fell from 13th to 17th in this week's rankings. Rocco Mediate remained at 18th, while Romero jumped into the 19th slot. Angel Cabrera dropped one space to 20th.