Atwal, who had a 70 in the first round, opened with a birdie on the first and followed it up with two more on seventh and ninth to turn in three-under.
Bogeys on 10th and 13th threatened to derail his challenge before birdies on the 14th, 16th and 17th ensured he was four-under for the day and six-under for two days.
Mark Wilson, who was eight-under through 11 holes, posted a career-best 10-under 62. He was incidentally playing with Harrison Frazar, who in the past has shot 59.
Wilson now shares the lead with Ben Crane (65) and David Toms (63) at 16-under 128 after 36 holes as low scores continued to dominate the tournament.
But the day's best score was a 11-under 61 from Ryan Moore, who tied the course record at the Nicklaus course. The tournament is played on three courses, the Nicklaus Private, Palmer West and Palm Springs.