Jeev slotted four birdies against a couple of bogeys, while Atwal managed three birdies against two dropped shots.
It was not the best of starts for Jeev as he stumbled to a bogey on the second but the Chandigarh golfer made amends with back-to-back birdies on the fourth and fifth holes to make the turn one-under.
On his way back, Jeev picked up two more shots on the 12th and 17th holes before dropping a stroke on the 18th.
Meanwhile, Atwal, a 10th tee starter, made up for a rather subdued back-nine by playing out a flawless front nine studded with two birdies.
The Orlando-based golfer's back-nine was a slightly disappointing affair as he managed just one birdie against two bogeys.
At the top, American Brent Delahoussaye took a two-stroke lead with a sensational eight-under 62. Delahoussaye's compatriots Vance Veazey and Brock Mackenzie followed him a couple of strokes behind at the tied second spot.