Fowler, who was fifth overnight, closed the round with an 11-under 61 to move to 18-under, four shots more than Hoffman who led for the past two days before fumbling when it mattered most.
Hoffman carded a par-72 to lose out to Fowler on the final day by four shots.
Fowler took home USD one million for his fine win and the tournament trophy was presented by Hero Motocorp chairman Pawan Munjal and tournament host Woods on the 18th green.
Tommy Fleetwood (67) and Jordan Spieth (69) Tied-3rd at 12-under and defending champion Hideki Matsuyama (68) was Tied-5th with Patrick Reed (68) and Justin Rose (70).
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Francesco Molinari (70) was ninth and Woods, (68) completed the Top-10 alongside Matt Kuchar (71).
After a windy round three, conditions were better for the final round. Seven straight birdies by Fowler and the excitement in Albany was palpable. By the end he had cruised along to a new tournament record and admitted to having thoughts of a 59 as he was 8-under through nine and 9-under through 11.
"Obviously I knew I needed to get off to a hot start today to give myself a chance, and Charley's been playing some solid golf and I wasn't expecting him to come back to me.
"I knew I was going to have to go out and get him. Like I said, get off to a decent start and at least show my face a little bit. I wasn't expecting seven out of the gate, but I'll take it," said the winner.
The atmosphere turned electric when Woods smashed his driver on the 336-yard par-4 seventh and drove the green with the ball finishing some 25 feet away. He read it well and the ball curled it way into the cup for an eagle and he was up to 4-under for the round.
A birdie after coming out of the bunker on ninth, which he eagled on second day, meant a 5-under 31.
He rebounded with a two-putt birdie on par-5 11th and then made a nice par save on 12th.
Once again he nearly drove the green on par-4 14th and the birdie there saw him back at 5-under. The birdie on the par-5 15th saw him to rise to 6-under for the day and 10-under for the tournament.
It seemed double digits under par on a comeback was surely on the cards before he bogeyed par-3 17th with a 10- footer par miss.
Woods, however, was pleased with his performance during the week.
"I was still a little scratchy with my irons, drove it pretty good all week, made some good putts. Overall I'm very pleased. I showed some good signs. I'm ready for a bright future," he said.
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