On another low-scoring day at TPC River Highlands in Cromwell, Connecticut, Bradley built a 21-under par total of 189 as Reavie posted a seven-under par 63 for 190.
It was a further four strokes back to world number four Patrick Cantlay, who had nine birdies in his nine-under 61 for 194.
Rickie Fowler went one better with a 10-under par 60 and headed a trio on 195 that also included Adam Scott, who shot 65, and overnight co-leader Denny McCarthy, who settled for an even par 70.
Bradley and Reavie, playing together in the final group, had traded the lead and were tied at 20-under through 15 holes when Bradley landed his tee shot at the par-three 16th six feet from the cup and converted the birdie.
Reavie, meanwhile, missed the green and was unable to get up and down, falling two adrift. He clawed back a shot with a 12-foot birdie putt at 18, where Bradley couldn't get his 18-foot birdie attempt to drop.
"It was just really solid," Bradley said. "Pretty boring honestly until the very end there. I made some nice shots some nice putts. I'm proud of the way I played."
Bradley, born in Vermont and a favorite of New England fans, admitted had to battle a tendency to push too hard in a tournament he has long wanted to win.
"I've wanted to win this tournament forever, so the feeling of wanting to push and win is something I need to fight against and just let myself go out and play," he said.
Birdies to win
Bradley, who shared the overnight lead with McCarthy, quickly built on his advantage with three birdies in the first six holes.
But he parred the next six as Reavie continued to pile on the pressure that started with his 24-foot birdie at the first.
Reavie added birdies at the sixth, seventh and eighth. Another run of three straight from the 11th through 13th saw him pull level then move in front of Bradley - who regained a share of the lead with a 16-foot birdie at the 15th.
Reavie said his birdie at the last was "huge, just to get a little momentum going to dinner and sleeping tonight.
"I played well - really well in the middle of the round," Reavie said. "Then pulling that nine-iron on 16, I know you can't hit it over there. Just a bad swing."
Reavie predicted the final round would be a "shoot-out".
"You've got to make birdies and eagles to win this golf tournament," he said.
Fowler showed there were plenty to be had with eight birdies and an eagle in his 10-under effort
But his bid to break 60 came undone at his final hole,the ninth, where his approach hit the green and rolled into the first cut of rough and he settled for a par.
