Wallace added a flawless 65 to his opening 68 at Jumeirah Golf Estates to reach 11 under par, a shot ahead of former Masters champion Danny Willett, Jordan Smith and Adrian Otaegui.
Current Masters champion Patrick Reed is two shots off the lead after a 66 compiled in the company of Rory McIlroy, whose 67 left him a stroke further back alongside Tommy Fleetwood, Kiradech Aphibarnrat and Dean Burmester.
Fleetwood needs to win the season-ending event and see Ryder Cup partner Francesco Molinari finish outside the top five in order to retain his status as European No 1, a scenario which looked unlikely when the latter carded an opening 68.
However, the Open champion struggled to a 73 to end the day in a tie for 27th on three under, six shots behind Reed in fifth place.
Wallace was fined £3,000 for taking too long over a par putt on the ninth hole on Thursday and would have faced a one-shot penalty for any further transgressions, but stayed within the time limits and birdied four of his last five holes.
Seven more birdies yesterday took the 28-year-old to the top of the leaderboard and he had no issues with the slow-play situation as he seeks the biggest win of his career and a fourth European Tour title of the season.
Wallace – who was fifth in Sun City last Sunday – said: “I’ve got rid of all the expectations that have come with playing well and winning. I’ve expected higher from myself and that’s just killed me.
“So I’m playing with freedom now and trying to place as high as I possibly can come the back nine holes on Sunday and then that’s when I normally will try and kick in and want to win a tournament, depending on where I am.”
Fleetwood was the “last man on the range” on Thursday after scrambling to an opening 69, but struck the ball much better in a 67 that included twice three-putting for par on par fives.
“It’s still a very difficult task to win the Race to Dubai, it’s not like I’m a prolific winner this year,” Fleetwood said.
“I’ve had chances and missed them so I am still trying to knock on that door and win a tournament – just the same as everybody is.
“There’s so many different things going on, but the situation is pretty black and white.
“Just keep going and put everything into it for another two days.”