'I've worked pretty hard for this,' said Singh. 'I finally achieved what I wanted to do starting at the beginning of the year.'
Woods, who held the No. 1 ranking for 264 consecutive weeks, posted a 69 to tie for second along with last year's champion Adam Scott at 13-under-par 271.
Singh, who had been closing in on the top spot in the rankings throughout the summer, carried a three-shot lead into the final round at the TPC of Boston. Playing in the last group with Woods, Singh needed to finish ahead of his playing partner to move into the No. 1 position and did just that despite blowing his lead on the inward half.
'My main goal starting the day was to go out there and win the golf tournament,' said Singh. 'It was a golf tournament to me. It wasn't about the ranking. It wasn't about going out there and trying to beat Tiger and beat the No. 1 player. I was out there trying to win the golf tournament and that was my goal starting out today.'
Singh was in control early after his approach to the par-4 first stopped within 6 feet of the cup. He stumbled to a bogey at the very next hole, however, and found trouble again with a bogey at the par-4 sixth, but managed to stay on top.
Woods struggled with a bogey at the second and broke his wedge in the process, but he countered with a birdie at the par-4 fifth. He hit an errant drive at the par-5 seventh and missed a 5-foot par putt to fall back to 10 under.
The 28-year-old recovered again at the following hole and hit his tee shot to 6 feet for a birdie at the par-3 eighth. Woods then knocked his second shot to 12 feet at the ninth and ran home the birdie putt to move within one of Singh.
Singh persisted and landed his approach within 5 feet of the hole for a birdie at the par-4 10th. Woods was scrambling at the par-4 12th but chipped in for a birdie to reach minus-13 before a mistake by Singh at the following hole briefly forged a tie atop the leaderboard.
The Fijian bogeyed the 13th to fall back into a tie with Woods, but Woods was unable to take advantage and three-putted for a bogey at the par-4 14th. Singh then played his approach inside 6 feet for a birdie at the par-4 15th to pull two ahead.
'I ran my putt by. It's hard to read the putts in the shadows there,' Woods said of his problems on the 14th green. 'I couldn't see whether it was flat or downhill.'
Singh, who won the PGA Championship last month, parred his next two holes before sealing the deal at the par-4 17th. He knocked his second shot to 25 feet and drained the birdie putt to regain a three-shot advantage over Woods.
Woods had a birdie try of his own at the 17th, but was unable to convert. Singh then hit his second shot to the back of the green at the par-5 18th and two-putted for birdie to cap off his 21st career victory on the PGA Tour.
'I thought I was playing good enough to be No. 1 for a while, but obviously the ranking...I can't do anything about the ranking,' said Singh, who pocketed $900,000 for the win. 'Finally it's turned into my favor.'
Woods had spent 334 weeks overall atop the rankings, but a drought in the majors and a lone victory this year has dropped him from the top. Always a competitor though, Woods welcomed the challenge of regaining the No. 1 ranking.
'Vijay and I have gone head-to-head many times and hopefully we can do it again,' said Woods.
Scott, who earned his first career victory on the PGA Tour at this event last year, tallied a pair of birdies and a bogey over his first nine holes. The young Australian caught fire on the back side with four straight birdies, starting at the par-4 10th, and added a birdie at the last for a round of 65.
'It was a really slow start,' said Scott. 'Making the turn it was just another day out there. Things sparked up a bit, and when that happens, you've got to go with it because you never know what can happen out here.'
John Rollins shot a 66 to join Daniel Chopra in a tie for fourth at 10-under-par 274. Hank Kuehne and Shigeki Maruyama were one shot further back at 9-under-par 275.
Jay Williamson took eighth place at 8-under-par 276. Brad Faxon, Charles Howell III and Bill Haas followed at 7-under-par 277.
David Duval posted a 67 on Monday to finish in a group at 5-under-par 279.