Jim Furyk was at 69, with three players at 70: defending champion Sergio Garcia, Robert Allenby and Ernie Els.
The greens were hard and fast at Gary Player Country Club because of little rain this month in this part of South Africa.
DiMarco, winner of the Phoenix Open, had one bogey -- on the sixth hole, the shortest par 4 on the course. Goosen, the 2001 U.S. Open winner, played a bogey-free round but was not satisfied with his game.
'I had a lot of chances for birdies coming in, but I just don't feel comfortable over the ball at the moment,'' he said.
Furyk, who was disqualified in last year's first round for a violation he called on himself, played before enthusiastic galleries.
'A lot of people told me they were glad to have me here, and it sure was nice to have the support of people in Ernie Els' back yard,'' he said.
Nick Price and Michael Campbell were at 71 in the 12-player field. Darren Clarke and Padraig Harrington were at 72, with Bob Estes at 73 and Colin Montgomerie at 74.
Full-field scores from the Nedbank Golf Challenge