Atwal, who has had a tough time this season, missing more cuts than he has made, is now one-under 139 for two rounds on the par-70 Old White TPC Course.
Daniel Chopra missed the cut with a second round 74 after his first round 69.
Atwal had a bogey on the seventh but made up with birdies on 11th and 12th but a bogey on 13th placed him in the danger zone.
He hauled himself back to safety with a long birdie putt on the final hole to survive the cut.
But the big news was Tiger Woods missing the cut at the same event a week after winning his third title of the season.
Woods shot 71 and 69 and it was only ninth missed cut in his entire year.
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Also missing the cut was Phil Mickelson, making it the first time the two have missed the cut in the same tournament as professionals.
When Woods was an amateur, he and Mickelson missed the cut at the 1993 Byron Nelson.
US Open champion Webb Simpson moved to the top of the leaderboard at nine-under as play was halted earlier due to darkness on ad ay when play was also delayed due to rain.
First round leader, Vijay Singh dropped down the leaderboard with a second round 74 after a first round 63.