Herbert closed with four pars to hold off Danny Lee (71) and Patrick Reed, who finished with four Birdies over his last six holes for a 65 and then waited to see if it would be enough.
Herbert, the 25-year-old Australian who won the Irish Open earlier this year, stayed in front by closing with two good par saves and missing a pair of 7-foot birdie attempts he didn't need.
His first PGA Tour victory, and third worldwide, sending him to the Masters for the first time.
“It opens up so many doors,” said Herbert, who earned his PGA Tour card through the Korn Ferry Tour Finals two months ago. He had missed the cut in his other two starts this season.
The wind and rain, which caused tee times to be moved up, was as fierce as advertised, and play was halted briefly without having to bring the players off the course.
“I felt like I grinded really well early and I had the right attitude going into the day that it wasn’t going to be easy,” Herbert said. “You just knew it was going to be one of those days where you had to battle really, really hard. Under par was going to be a great score.”
He finished at 15-under 269.
Taylor Pendrith of Canada, who started the final round with a three-shot lead, failed to make a Birdie in closing with a 76 to tie for fifth.
It was a record-setting week at the Butterfield Bermuda Championship as four new marks were established, led by Pendrith’s second round 61 (-10), which was a new tournament and course record. In addition, 12 records were tied, including the lowest back nine score of 29, which was equaled by Bermuda’s own Camiko Smith to start his second round.