The 43-year-old Fijian, three strokes clear overnight in the season-opening event and armed with a new belly putter this week, closed with a three-under-par 70 at a breezy Kapalua Resort.
Singh looked in cruise control as he stretched his lead to five with seven holes to play before his advantage was trimmed to two when Scott holed a 10-foot birdie putt at the 16th.
The Australian's challenge effectively ended, though, with a three-putt bogey at the par-four 17th and he had to settle for second place after completing a seven-birdie 69.
Singh, who failed to birdie the par-five last for the fourth day in a row, finished on 14-under 278 to move past Sam Snead as the PGA Tour's most prolific winner after the age of 40.
Singh and late American Snead had been level with 17 titles apiece at the start of the week.
"All wins are important but this one gives me a lot more freedom from here on," a smiling Singh told reporters after earning a cheque for $1.1 million.
"I don't have to force myself. Sometimes when you don't win for a while, in the back of your head you have some kind of pressure," added the Fijian, who had triumphed only once in his previous 35 PGA Tour starts.
"I wanted this win, and I practised hard for it. Hopefully, it doesn't stop there. I feel good and I'm looking forward to the season."
Scott, who birdied the final hole to secure outright second place, knew he was up against it when Singh pulled five shots clear early on the back nine.
"I was kind of leaving it all a little late," the 26-year-old said. "That second putt on 17 was a bad one and that was it really.
"Vijay was pretty much in control and I didn't think he would do anything silly at the last."
South Africa's Trevor Immelman, the Tour's 2006 rookie of the year, finished third at nine under after returning a 72.
Americans Davis Love III (68), Will MacKenzie (72) and J.B. Holmes (72) were a further stroke back in a tie for fourth.
Compatriot David Toms fired a best-of-the-week 67 to share eighth place, and Australia's Stuart Appleby, bidding for a fourth successive victory at Kapalua's Plantation Course, finished joint 13th after a 72.
Former world number one Singh, runner-up here twice in the previous three years, made a fast start to the final round.
He struck his wedge approach to just five feet at the par-four first to set up birdie number one and picked up another shot by holing an eight-footer at the difficult par-three second.
The three-times major winner then parred the next seven holes to reach the turn in two-under 34.
Although his putter failed him a few times over the closing stretch, he rolled in a 15-footer to birdie the par-three 11th for a healthy five-stroke cushion.
Scott's late surge provided some drama but Singh always had enough in reserve to seal the first victory in the PGA Tour's much-trumpeted new era of golf.
This week's event launches the inaugural FedExCup, a season-long points competition culminating in a four-event playoff series with $10 million to be won by the overall champion.
"I left a lot of putts out there, but I'm glad that I ended up winning," said Singh, who heads the first instalment of the Cup standings with 4,500 points.