Woods begins his record 335th week as the world No. 1. Greg Norman owned the previous record of 331 weeks.
Singh dropped to No. 2 just ahead of Ernie Els. Els eagled the 72nd hole Sunday to win the Dubai Desert Classic for the third time. He is just 1.05 points behind Woods for the top spot in the rankings.
Phil Mickelson, who finished second behind Woods at Doral, remained fourth in this week's rankings. Reigning U.S. Open champion Retief Goosen held on to the fifth spot, while Sergio Garcia stayed put at sixth.
David Toms, who won the WGC-Accenture Match Play Championship two weeks ago, continued to rise in the rankings as he came in seventh this week, up from ninth one week ago.
Padraig Harrington remained eighth, while Adam Scott slid two spaces to ninth. Stewart Cink and Mike Weir exchanged places from last week as the American climbed to No. 10, while the Canadian slipped to 11th.
Davis Love III held onto the 12th position and was followed again by Mercedes Championships winner Stuart Appleby and Chris DiMarco. Miguel Angel Jimenez, runner-up to Els in Dubai, moved up one space to 15th, while Darren Clarke dropped one spot to 16.
Chad Campbell stayed put at 17 and was followed by Luke Donald and Justin Leonard, who respectively held on to the 18th and 19th positions.
Stephen Ames climbed one slot to close out the top-20 this week. To make room for Ames, last week's No. 20 Kenny Perry dropped one space to 21 this week.