Americans Chad Campbell, Joe Durant, Jeff Maggert, Scott Langley and Eric Axley carded 64s while 2010 winner and reigning Masters champion Bubba Watson opened with a 67.
Steele, who won his only PGA Tour title at the 2011 Texas Open, made a sizzling start as he holed out from 129 yards to eagle the par-four first.
He then birdied the second, seventh and eighth, where he drained a 27-footer, to reach the turn in five-under 30 before picking up further shots at the 11th, 12th and 13th.
“The thoughts crept in,” Steele, 31, told reporters about the opportunity to shoot a 59 with three more birdies required over his last five holes. “If they don’t creep in, do I shoot 59, do I shoot 65?
“It definitely was in the back of my mind, so probably amped me up a little bit more, so made everything a little bit tougher.”
Steele was delighted, though, to reap reward on Thursday after playing some good golf over the past few months without getting the scores he felt he deserved, including missed cuts in his previous two tournaments.
“I haven’t been getting a lot out of it,” said the Californian, who has recorded just two top-10s in 18 starts on the 2013-14 PGA Tour, his best finish a tie for sixth at the Phoenix Open in February.
“I felt like I was really playing well at Byron Nelson and at Memorial and missed both cuts. I was just getting a little sloppy, a little lazy behind the ball, not seeing the shot, not getting into it the right way.”
American world number five Matt Kuchar opened with a 66 while compatriot Ken Duke, who won last year’s Travelers Championship in a playoff with Chris Stroud, returned a 65.
Australian Oliver Goss, one of four players in the field making their professional debuts this week, carded a 70. Erik Compton, a double heart-transplant recipient who tied for second at the U.S. Open four days ago, posted a 74.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Frank Pingue)