SAN ANTONIO—Australia’s Nathan Green shot an 8-under 62 on Thursday to take a two-stroke lead over Olin Browne and Paul Claxton in the Texas Open.

Green, winless in three seasons on the PGA Tour, birdied nine of the first 16 holes before dropping a stroke on the par-3 17th and closing with a par.

“I didn’t feel really good before the round started and then on the first hole I snapped my drive, it hit a rock and bounced back in the fairway,” Green said. “From there, everything went pretty well.”

Claxton and Browne, a three-time tour winner, had bogey-free 64s...

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