Singh trailed by two strokes entering the final round, but overtook Harrison Frazar and John Huston with birdies on four of his first five holes. Singh went on to shoot a 6-under 29 on the front nine of the Stadium Course at TPC at Scottsdale, one stroke off Chris DiMarco's nine-hole course record of 28.
Huston, who finished second, vaulted up 28 spaces to 40th in the latest rankings.
Tiger Woods is still in first place in the rankings while his knee rehab continues. Woods is expected to return to the course for the first time in March. Ernie Els remains second in the latest rankings while Phil Mickelson stayed put in third after tying for ninth place in Phoenix.
Retief Goosen dropped one spot to fifth. David Toms and Sergio Garcia also fell one spot to sixth and seventh, respectively. Padraig Harrington remains in the eighth slot.
Davis Love III exchanged positions with DiMarco to come in at No. 9.
The next six spaces stayed the same. Colin Montgomerie came in at 11th, while Jim Furyk, Nick Price, Rocco Mediate, Robert Allenby and Angel Cabrera ranked 12th through 16th.
Justin Leonard and Rich Beem flip-flopped the 17th and 18th spaces while Michael Campbell and Bob Estes each climbed one spot to 19th and 20th, respectively.
Lian-Wei Zhang, who defeated Els in Singapore at the Caltex Masters, climbed 46 places to No. 96 to become the first Chinese player to crack the top 100 in the World Rankings.