Bart Bryant jumped to No. 137 in the world courtesy of his win at the Texas Open.
Tiger Woods, Ernie Els and Phil Mickelson remained in the second through fourth positions behind Singh.
Davis Love III, who went 1-3-1 in the Ryder Cup, moved up one slot to No. 5, while Retief Goosen slipped to sixth. Mike Weir, Padraig Harrington, Adam Scott, Stewart Cink, Jim Furyk, Sergio Garcia and Stuart Appleby remained in the seventh through 13th positions.
Darren Clarke, who went 3-1-1 for the winning European Ryder Cup squad, inched up one slot to 14th in this week's rankings. Chris DiMarco, the top point earner for the United States Ryder Cup team, jumped two spots to 15th.
Kenny Perry stayed at No. 16 in this week's rankings, while Chad Campbell fell three spots to 17th. Todd Hamilton remained at 18 and Scott Verplank moved back into the top-20 at No. 19.
Spaniard Miguel Angel Jimenez held on to the 20th spot in the rankings. Stephen Ames tumbled three spaces to come in at No. 21 this week.
1. Vijay Singh (Fiji) 13.35
2. Tiger Woods (USA) 12.07
3. Ernie Els (SAfr) 11.19
4. Phil Mickelson (USA) 8.65
5. Davis Love III (USA) 7.40
6. Retief Goosen (SAfr) 7.28
7. Mike Weir (Can) 6.85
8. Padraig Harrington (Ire) 6.29
9. Adam Scott (AUS) 5.20
10. Stewart Cink (USA) 4.94