The 35-year-old shot four birdies and three bogeys, allowing in-form South African James Kingston and Adam Groom of Australia to catch him on eight-under 136.
"I just didn't putt well enough today," Moe told reporters. "But I'm confident I'll bounce back tomorrow."
Kingston, 37, lies 12th on the European Tour's money list after losing in a playoff to his compatriot Darren Filchardt at this month's Qatar Masters.
Groom, who started from the 10th tee, was 10-under for the tournament after seven holes on Friday but made a double-bogey on the par-five 18th.
Just one shot back, in joint fourth place, was India's Jyoti Randhawa, Asia's best golfer last year and a perennial favourite at the par-72 Delhi Golf Club, where he won back-to-back Indian Masters titles in 1998 and 1999.
Randhawa followed up Thursday's six-under 66 with a round of 71.
The 30-year-old started with a birdie on the second hole but three-putted on the third for bogey and drove into the bushes for a double-bogey on the fourth.
He recovered, however, with birdies on the 14th and 18th holes.
"Things could have gone a lot better for me, that's a positive," Randhawa said. "But after two days, seven under, one shots behind the leaders - I would've taken that."
Also on 137 was Canadian Rick Gibson, runner-up last year to India's Vijay Kumar, who missed the cut by with shots with a two-day aggregate of 146.
Gibson made four birdies and four bogeys in an up-and-down round he described as "scrappy".
The day's best card of 66 was returned by American Alex Rodger and New Delhi's Gaurav Ghei.
Arjun Atwal, who is ninth in Europe after beating European number one Retief Goosen of South Africa to win last month's Malaysian Open, had 36 putts in a round of 72 that put him on three-under 141 at the halfway stage.
"I putted badly, what more can I say," Atwal said. "I'm five shots behind but I'm not giving up, I still believe I can win this."
