Els and Goosen are joined atop the leaderboard by world No. 13 Stuart Appleby and world No. 24 Lee Westwood to pace the 12-player field. Chris DiMarco and Nick Price are one stroke back at 1-under-par 71.
Bogeys at three and eight got Els off to a tough start. He started to turn things around with a birdie on No. 9 at The Gary Player Country Club Course.
The South African came right back to birdie the 10th to reach even par, then birdied the par-5 14th to get into red figures at 1 under. He moved to minus-2 with a birdie at 16 and parred his final two holes to stay there.
Goosen had an up-and-down front nine. He got off to a quick start with birdies at the first and second, but faltered with a bogey at the third. His troubles continued with bogeys at five and six that dropped him to plus-1.
The reigning U.S. Open champion moved back to even par for his round with a birdie at the ninth. Goosen ran off seven straight pars from the 10th, and closed with back-to-back birdies to tie for first.
Appleby stumbled to a bogey at the third, but came back to birdie seven and nine. Around the turn, the Australian moved to 2 under with a birdie at the par-3 12th. An eagle at the par-5 14th put Appleby in position to take the overnight lead, but he closed with consecutive bogeys to slip back to 2 under.
Westwood got going with birdies at two and seven, then stumbled to bogeys at eight and nine but atoned for those mistakes with birdies at 10 and 11. He dropped back to minus-1 with a bogey at the 14th and moved into a share of the lead with a birdie at the last.
Jim Furyk and Todd Hamilton share seventh place at 2-over-par 74. Defending champion Sergio Garcia struggled to a 3-over-par 75, and shares ninth place with Jay Haas and Fredrik Jacobson. Chad Campbell is well off the pace at 8-over-par 80.