The four-day event features 18 of the world's top players competing for the richest first-place prize in professional golf, $1.2 million.
Perry's round of 65 Thursday included eight birdies and one bogey, while Singh played a bogey-free round with seven birdies. Both players birdied the 18th hole at the par-72 Gary Player Country Club.
Scores were generally low, as overnight rain softened the greens and allowed the players to take more aggressive shots.
'The pins were in generous positions and good scoring was possible if you put the ball in the right places,' said Singh.
Robert Allenby and Adam Scott of Australia, Chris DiMarco of the United States and Northern Ireland's Darren Clarke are all one shot back after carding six-under 66s.
Stuart Appleby and Jerry Kelly both shot 67s in the first round, while Stephen Leaney, Sergio Garcia and Tim Clark finished the opening 18 holes three strokes off the pace. Three-time winner Nick Price stands at three-under par.
Defending champion and world No. 3 Ernie Els struggled with an even par 72, marking the first time that he has failed to break par in 29 rounds at Sun City. Els has captured this event three of the past four years.