Fellow American Kelly Kraft, who made a hole-in-one from 174 yards at the par-3 fifth hole, was second at eight-under with three holes remaining when play was called for the day in fading light.
Now in his second year as a full-time PGA Tour member, Spaun said he was ready to take the next step in his career.
"I’ve had a year’s experience now on the tour and this year it’s kind of just taking my game to the next level instead of being someone who lingers around the cut or top-20s," the 27-year-old told reporters.
"It’s time to step up if I want to do something big out here on tour and make a name for myself."
Robert Garrigus also made a big move to reach seven-under and third on the leaderboard thanks to his 65, which could have been even better but for a double bogey at his ninth hole.
"It was a lot of fun," Garrigus said. "I really didn’t swing as good as I wanted to but the putter worked really well today which can cure a lot of things.
"All in all it was a great day with eight birdies. I’m going to cherish this one."
Australian Aaron Baddeley and Patton Kizzire each fired 66s to move to six-under.
This week’s event is the sixth of 45 on the 2017-18 PGA Tour schedule.
(Reporting by Jahmal Corner, editing by Nick Mulvenney)
