Appleby shared the first-round lead with three others in the 12-player field.
One of those first-round co-leaders, Lee Westwood, carded his second straight 2-under 70. He is alone in second place at 4-under-par 140. Nick Price (70) shares third place at minus-3 with first-round co-leader and U.S. Open champion Retief Goosen (71).
Appleby, who closed round one with bogies on 17 and 18, began his second round with a birdie at the par-5 second. He moved to 4 under with a birdie at the fifth at The Gary Player Country Club Course.
The 33-year-old tripped to a bogey at the eighth. However, Appleby bounced right back with a birdie at No. 9. He made it two in a row when he birdied the 10th and then parred his final eight holes to remain at 5 under.
'The ball went further today because the weather was a lot hotter, but the course is still very tricky,' Appleby said. 'I felt my putting was a lot better today, I hit some quality putts.'
Westwood carded two birdies and two bogeys over his opening five holes. The four-time European Ryder Cupper ran off three straight birdies from the par-4 eighth to jump to 5 under.
The Englishman picked up another birdie at the par-5 14th. Westwood then faltered to a double bogey at the 17th to drop back to minus-4.
'The driving areas are very tight and the penalties for missing are very harsh,' said Westwood. 'Plus the firm greens make it difficult to get close to the flags, so 70 is a great round now. I played pretty good, solid golf and I see no reason to change my strategy.'
Ernie Els, who shared the first-round lead, struggled to a 2-over 74. He stands alone in fifth place at even-par 144. Chris DiMarco matched Els' 74 and is one stroke behind him at plus-1. Todd Hamilton is behind DiMarco at 2-over-par 146 after a 72.
Jay Haas stands in eighth place at 5-over-par 149 after a 74. Jim Furyk, the 2003 U.S. Open champion, struggled to a 4-over 76 to fall to 6-over-par 150. Sergio Garcia, the defending champion, is in 10th place at 7-over-par 151 after a 76.
Fredrik Jacobson (plus-9) and Chad Campbell (11-over-par 155) are well off the pace.