"I didn't think I could make it into the Tour Championship, and I certainly didn't think I could win," Bryant said. "I feared choking my guts out all week long."
Starting the final round with a three-shot lead, Bryant birdied three of the first six holes to double his advantage and easily survived a mid-round challenge from Woods to clinch his third victory in the past 14 months.
This one was worth 1.17 million dollars and bumped him to ninth on the money list. Not bad for a 42-year-old who never had previously won on the PGA Tour.
"I'm thrilled beyond description," said Bryant, whose closing 67 gave him a tournament record of 17-under-par 263.
A medium-length, straight hitter, Bryant led the field in both fairways hit and greens in regulation. His game was ideally suited to a bone-dry East Lake course with plenty of roll, and the mental resilience he displayed to cope with the pressure of leading after every round was perhaps even more impressive.
Bryant needed the cushion, because bogeys at the fifth and sixth holes gave his rivals a glimmer of hope.
The dropped shot at the par-three sixth could have been worse, because he found the water short of the green and did well to limit the damage to one stroke by sinking an eight-footer.
Retief Goosen, who started the day in second place, was off his game, leaving it to Woods to provide the only real threat.
But even Woods was too far back to mount much of a challenge.
He picked up three birdies in four holes midway through the round, but Bryant matched him and had the luxury of cruising to victory by playing the final six holes in one-over.
Woods, who shot 69, paid tribute to the winner.
Bryant will celebrate his career season by undergoing arthroscopic surgery on his left knee Tuesday. Next year, he will be exempt for all four majors for the first time and is looking forward to The Masters, which he has never played.
Down the leaderboard, consistent Scott Verplank (69) finished third at 271, while Goosen (74) faded to a tie for fourth with Davis Love (69) and Vijay Singh (67), another two shots back.
FINAL-ROUND SCORES (USA unless noted):
263 - Bart Bryant 62-68-66-67
269 - Tiger Woods 66-67-67-69
271 - Scott Verplank 67-66-69-69
273 - Retief Goosen (RSA) 64-66-69-74, Davis Love 68-71-65-69, Vijay Singh (FIJ) 69-69-68-67
274 - Stuart Appleby (AUS) 70-65-71-68, Ben Crane 68-65-72-69, Padraig Harrington (IRL) 71-66-68-69, Adam Scott (AUS) 73-69-65-67
275 - Mark Calcavecchia 72-69-68-66
276 - Sean O'Hair 73-73-64-66
277 - Jim Furyk 70-70-67-70
278 - Olin Browne 70-67-71-70, Luke Donald (GBR) 70-67-70-71, Tim Herron 73-68-71-66
279 - Chad Campbell 72-68-70-69, Chris DiMarco 69-72-67-71, Ted Purdy 71-69-69-70
281 - Sergio Garcia (ESP) 66-72-71-72, Kenny Perry 65-73-71-72
282 - Tim Clark (RSA) 67-67-72-76, David Toms 72-72-68-70
283 - Fred Funk 71-72-70-70, Charles Howell 67-68-70-78, Billy Mayfair 72-69-71-71
284 - Brandt Jobe 73-71-70-70
287 - Justin Leonard 70-74-71-72
289 - Lucas Glover 72-70-73-74.