Erlandsson owns a 1-stroke lead over Pablo Martin, who won last week's Alfred Dunhill Championship, and Dawie Van der Walt. Anders Hansen is in fourth place at 6-under and Richie Ramsey is another stroke back.
The South African Open, contested at the Pearl Valley Golf Estates, is part of the 2010 schedule of the European PGA Tour.
Erlandsson was in the second group off on the back nine and the early tee time may have slowed him as he was just 2-under after nine holes.
On the front side, he picked up six strokes in a six-hole span from Nos. 2-7. That included a 3-wood second shot on the par-5 fifth hole that got Erlandsson within 3 feet of the hole.
Martin finished his round with a 3 at the 601-yard 18th hole, with a 265-yard second shot getting him within striking distance of the eagle.
Van der Walt had a pair of eagles, matching Erlandsson's effort on the fifth hole and chipping in for a 2 at the 386-yard 10th hole.
Swim Week Miami Beach 2014 [PHOTOS]