Taking advantage of preferred lies on a rain-softened layout at the TPC Four Seasons Resort Las Colinas, the 26-year-old American piled up 10 birdies and an eagle at the par-five seventh to grab a three-shot lead in the US Tour event.
Winner here in 2011 before going on to claim his first major title at the US PGA Championship just three months later, Bradley covered his final nine holes in six-under 29 after storming home eagle-birdie-birdie.
Former Masters champion Charl Schwartzel of South Africa opened with a seven-birdie 63 while Americans Harris English and Ted Potter Jr. and Swede Robert Karlsson carded 64s.
"Today I matched up unbelievable ball-striking with great putting, which is very rare," Bradley told Golf Channel after hitting 15 of 18 greens in regulation and totalling only 24 putts on a course softened by overnight rain.
"You needed to go out this morning and shoot a good number if you could. I drove the ball great so I had the ball in my hand pretty much every hole. And I was hitting some really good iron shots. It felt really good.
"Just a really fun round," added the American, who started his day at the par-four 10th. "It kind of felt like a Saturday morning round with my buddies."
Bradley tied the tournament record of 60 held jointly by Sam Snead (1957) and Arron Oberholser (2006) while improving on the course record of 61 shared by Cameron Beckman, Justin Leonard and Charlie Rymer.
Asked whether he had entertained thoughts of shooting a magical 59, Bradley replied: "Not really because I played my last three holes in four-under.
"But I made two bogeys that were pretty poor and I had two pretty big lip-outs so it could have (been a 59) but I guess any time you shoot 60 it could."
Bradley made a fast start with five birdies in his first seven holes before bogeying the par-four 18th to reach the turn in four-under 31.
Though he dropped another shot at the par-four first, he rebounded with birdies at the second, fourth and fifth before covering his last three holes in four under.
A three-times winner on the PGA Tour, Bradley has yet to taste victory this season despite recording five top-10s in 13 starts. His best finish was a tie for third at the Arnold Palmer Invitational in March.
"It's just real exciting, it's an exciting feeling," he said of his title prospects this week. "First and foremost, I want to try to win the tournament and this puts me in a good position to do that."
South African world number seven Louis Oosthuizen, the highest-ranked player in this week's field, opened with a four-birdie 67 while Germany's former world number one Martin Kaymer returned a 68.
Defending champion Jason Dufner, who sensationally clinched last year's title by one shot after sinking a 25-foot birdie putt on the 72nd hole, carded a level-par 70 playing in the company of fellow Americans Matt Kuchar (69) and Bradley.
China's 14-year-old Guan Tianlang, who made his second consecutive cut on the US Tour at the Zurich Classic of New Orleans last month, also started out with a 70, offsetting two birdies with two bogeys.
Competing this week on a sponsor's exemption, Guan has been one of the biggest talking points in golf since he became the youngest player to make the cut in a major championship at the Masters five weeks ago.
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