Bradley began the day two shots behind overnight leader Webb Simpson but birdied his first two holes to join the former US Open champion on six under par. Starting from the tenth, former US PGA champion Bradley holed from 20 feet for birdie and repeated the trick from 12 feet on the next before a run of four straight pars.
Simpson was among the later starters along with Open runner-up Henrik Stenson, five under after a flawless opening 65, and world number one Tiger Woods.
Woods, seeking an eighth win at Firestone Country Club, was four under after a 66 matched by fellow American Ryan Moore and England’s Chris Wood.
World number three Rory McIlroy, looking to replicate the fifth place finish of last year which kick-started his season, had bogeyed the last in a first round of 70 and remained level par after nine holes.
Bradley, who has been paired with Woods and former Ryder Cup captain Davis Love III for the first two rounds of next week’s US PGA Championship, birdied the 18th to reach the turn in 32 and claim the outright lead. And another birdie on the par-five second gave the American a two-shot lead over Simpson, who was an hour away from starting his second round.
McIlroy had dropped back to one over par after a string of pars was followed by a bogey on the fifth, where he failed to get up and down from just short of the green.