Drysdale and Lawrie both had a 66 at the West Course of the Wentworth Club while world No. 1 Rory McIlroy slumped to a 74 and found himself in 100th place.
Drysdale came to the par-5 18th hole one shot off the pace and his second shot sailed left of the green toward a stream. The ball bounced off a rock in the water and hopped back on dry land, from where Drysdale chipped to within 8 feet.
He made the putt for birdie to seize a share of the top spot at the European Tour's top regular-season event.
The co-leaders were one in front of Alvaro Quiros, Justin Rose, Niclas Fasth, Jamie Donaldson and Richard S. Johnson. Rose had to be treated with medication for vertigo prior to the round, but made it through the day without further problems.
McIlroy hit a ball out of bounds by 2 inches, suffered five bogeys and a double-bogey and became so frustrated he threw a club.
"It's very disappointing," said McIlroy, who is playing in Europe for the first time since October. "I feel like I'm playing pretty well and I've just got to go and shoot the scores."
McIlroy missed the cut in his most recent tournament, the Players Championship, and will need an excellent round Friday to avoid missing the cut this week.
If McIlroy does miss the cut and Luke Donald winds up among the top eight at this tournament, Donald will move past McIlroy into the top spot in the rankings. Donald shot a 68 Thursday and was tied for eighth.