Slightly calmer winds than during the opening round allowed for some low scoring and Pepperell took advantage with a five-under-par 67 to get to eight-under overall at the Emirates Golf Club.
Pepperell holds a narrow lead over defending champion DeChambeau, who matched Pepperell's round, Ryder Cup European vice-captain Robert Karlsson and South Africa's Dean Burmester.
After opening the year with two missed cuts in Johannesburg and Abu Dhabi, Pepperell said he has returned to some old drills and switched to a claw putting grip this week.
“It might look very technical with me but believe it or not in my mind it doesn't feel that way, at least certainly when I'm doing pretty good, because it's all about feeling,” he said.
“I think regardless of what your hands are doing on the grip, great putters tend to look quite comfortable. When I set this way I look more comfortable which, in my mind and I think in the viewer's mind, should be more confident.
“It's been very good the past two days and I've been surprised with how good it's been.”
American DeChambeau made a fast start with three straight birdies and recovered from a bogey at the sixth hole to take advantage of the par-five 10th.
A missed green led to another bogey at the 15th but he gained a stroke on the 17th to get back to seven-under.
Burmester, who was involved in car crash on Wednesday, mixed five birdies with a sole bogey for a round of 68, while Karlsson remained in contention with gains on the final two holes.
Overnight leader Thomas Pieters of Belgium had a day to forget, finishing with a second round 77 to make the cut but slumped to a share of 32nd place on level par.