Second at the start of the day, one shot from South Korean leader Kim Si-woo, Conners returned for the second day in a row a 66 (-6).
He finished with a total of 268 (-20) of two shots the American Charley Hoffman (270, -18) and three shots another American Ryan Moore (271, -17).
Kim was demoted to 4 th place with his card 72 (for) for a total of 273, five shots of the winner.
Conners, 27, has perfectly managed to wait two hours in a row for heavy rains.
He started his day with four birdies on the first five holes. He then chained four bogeys in a row, before taking the lead in the second half of the course with six more birdies.
“This fourth round was really special, I went through highs and lows, but I finished well, even if I do not really remember what happened in the last three holes,” explained Conners, past qualifying to participate in this event.
“It’s pretty surreal, I do not think I really realize what I’ve accomplished,” he insisted.
With the win, Conners earned his qualification for the Augusta Masters, the first Grand Slam event of the year, which begins Thursday.
Rickie Fowler and Jordan Spieth finished 17 th (278, -10) and 30 th (281, -7) respectively.