Grace, coming off an 11th place finish in his title defence at the Heritage, birdied three of the four par-fives on the TPC San Antonio Oaks Course.
His birdie at the par-five eighth marked the start of three birdies in a row, a burst that included a 25 foot putt at the ninth to salvage a birdie after his tee shot found the rough.
"I hit it right in the thick of stuff and managed to get a flyer," Grace said. "I think I hit a wedge from 180 yards, got it to the back level. Made 25-footer for birdie. That's the best birdie I made all day."
Grace played early and said the winds that can bedevil golfers at the Oaks were mild.
"There's gusting," added Grace. "The nice thing about this place, there's not that many trees out there. It's all more bushes.