The two home golfers, both past major winners, picked up a shot each as play in the DP World Tour event began early on Sunday in anticipation of the heavy tropical storm.
However, it was then interrupted for several hours before the field went out again for an hour, only to be sent scurrying back to the clubhouse as the heavens opened once more and the threat of lightning made play dangerous.
Oosthuizen, the 2010 Open winner, took the lead on the sixth hole with a birdie putt but then made a rare mistake and hit into the water on the seventh for a bogey and was 16-under-par when play was suspended.
The 2011 Masters winner Schwartzel, who has won three times previously at Leopard Creek, birdied the third hole.
Christo Bezuidenhout, who won the tournament three years ago, started the day five behind the co-leaders but cut their lead to three strokes as he sunk three birdies in his opening seven holes.
England's Andy Sullivan, who was also 10-under-par at the start of Sunday's action, hit two birdies but then a bogey at the eighth before play was suspended.