The Indian, who has one PGA tour win against his name was at that stage 10-under and in top-20 of the leaderboard.
He then dropped from tied 31st overnight to tied 44th, but still has a chance to make the all-important PGA Tour card for 2013.
Meanwhile, Daniel Chopra had an even more steep fall as he double bogeyed no less than three times in third round and fell to tied 66th with a round of 76.
Also tied at 66th was Bhavik Patel.
South Korea's Meen Whee Kim shot a 5-under 67 on Friday on PGA West's Jack Nicklaus Tournament Course to maintain a one-stroke lead after the third round.
The 20-year-old Kim had an 18-under 131 total in the six-round event, from where the final top 25 and ties will receive 2013 PGA TOUR cards.
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The next 50 and ties will earn Web.Com Tour cards.
Atwal had birdies on second, fourth and fifth before dropping a shot on eighth, which he quickly made up for on ninth. Another birdie on 11th saw him get to four-under.
He stayed there for next five holes before the bogey-bogey finish.
Fifth after second round, Chopra rose to third with a birdie on fifth, but a bogey on sixth and a double on seventh started the slide.
He birdied the 10th and 11th to indicate a revival, but double bogeys on 12th and 15th spelt total disaster.
Sweden's Robert Karlsson was second after a 65 at the Nicklaus course.
Edward Loar was 16 under after a 66 on the Nicklaus course, and two-time PGA TOUR winner Vaughn Taylor had a 69 on the Nicklaus course to top the group at 15 under.