Lawrence, who turned pro last October, got off to a quick start with three birdies over his first six holes to keep pace with Clark and eventually lead midway through the round.
'When I stood on the first tee, I thought it was going to be really difficult day for scoring because the wind was quite stiff,' said Lawrence. 'But when Tim was rolling in all those putts over the first couple of holes, I knew I had to start doing something as well.'
The 21-year-old, who posted two top-10 finishes this season, added two more birdies on the back nine to secure his lead at the Leopard Creek Country Club.
'I had a lot of putts which were downhill, so I had to be careful not to be too strong with them,' said Lawrence. 'But I just kept swinging away, and it was only coming down the 18th fairway that I started to feel a little tingly. But the reason is that it only occurred to me then that I can win this thing.'
Clark was poised to grab the lead on his own with four birdies on the front nine to make the turn at 11-under, but he ran into trouble with back-to-back bogeys from the 10th.
He remained calm and turned in three birdies over the remaining seven holes for a round of 67 of his own.
With 18 holes remaining Clark has all but wrapped up the Sunshine Tour Order of Merit. His closest challenger in the race for the money title, England's Justin Rose, carded a 1-under 71 to trail Clark by 10 strokes.
Clark, who earned his PGA Tour card last year after finishing third on the 2000 Buy.Com money list, missed most of the 2001 campaign due to a wrist injury. The 26-year-old was granted a medical exemption for 2002 but opted to finish out the season in his native country after capturing the South African Open.
The Order of Merit title will earn Clark an invitation to the British Open, the World Golf Championships American Express and the World Golf Championships NEC Invitational.
Overnight leader Bruce Vaughan bogeyed the opening hole and added two more bogeys at Nos. 4 and 5. The American settled down with three birdies on the back nine to move into third place at 10-under 206.
South Africa's Andrew McLardy (69) is four strokes off the lead at 9-under 207 while fellow countryman Nic Henning is one shot further back at 8-under.
Full-field scores from the South African Tour Championship