Atwal, who had six points in the first round and four more in second, made it on the cut line.
Meanwhile, Richy Werenski birdied six holes and eagled No. 18 to take a two-point lead.
The 25-year-old American had a 15-point round to reach 26 points for two trips around the high-altitude course at Montreux Golf and Country Club.
The scoring system awards eight points for double eagle, five points for an eagle, two points for a birdie and deducts a point for a bogey and three points for a double bogey or worse.
Play was delayed for more than an hour due to rain and lightning in the area.