Bradley, winner of the PGA Championship two years ago, posted the second 60 recorded on the tour this year and the 28th in the history of the circuit. He had never shot lower than 63 in his career.
He began on the back nine of the TPC-Four Seasons Resort course and reached the 18th hole, his ninth, in 5-under.
Bradley, however, bogeyed the 18th and also bogeyed the first after making the turn. He bounced back to birdie three of the next four holes and then finished in spectacular fashion by holing a 10-foot putt for eagle at the par-5 seventh and making birdie putts of 11 and 3 feet at the final two holes.
Charl Schwartzel, playing in the tournament for the first time, was alone in second after firing a 63. Those at 64 included Robert Karlsson, Ted Potter Jr. and Harris English. Angel Cabrera, who lost to Adam Scott in a playoff at the Masters last month, was in the group at 65.
Thursday's opening round was played in almost ideal conditions with 76 players breaking par. The course played easier than normal thanks to the decision by tour officials to allow players to clean the ball and place it on the fairway.
That became necessary after more than two inches of rain fell on the course during the storms that produced deadly tornadoes in the region on Wednesday.