Schwartzel, coming off an 11-stroke victory in Thailand last week, had six birdies and an eagle at the par-5, 541-yard 18th hole. Bourdy, the first-round leader, had an eagle but also his first bogey of the tournament en route to a 7-under 65.
The two players are tied at 13-under 131 after 36 holes.
They are four strokes ahead of Darren Fichardt, who had a 68 that left him alone in third at 9-under. Louis De Jager and Steve Webster, who each were 3-under 69 in the second round, are tied for fourth at 8-under.
Bourdy played the second nine of the Leonard Creek Golf Course first and was 2-under at the turn. He opened his second nine with back-to-back birdies but had a bogey at the third hole.
Bourdy had consecutive 2s -- a birdie at the par-3 fifth hole and a chip-in eagle at the 319-yard, par-4 sixth -- and a birdie at No. 8.
Schwartzel, also beginning on the 10th hole, was 2-under through seven holes. He then was 5-under over the next four holes, with a birdie at 17, an 18th-hole eagle and birdies at Nos. 1 and 2. A birdie at the fifth hole got him a share of the lead.