Goosen, who led the event after the first 18 holes Thursday, shot 4-under-par 68 in the second round. Green caught him after shooting a 7-under 65.
They have an overall score of 11-under-par 133.
"I birdied the second hole, but then lost my concentration on the fifth and suddenly I wasn't making anything," Goosen said on the tour's Web site. "But there are 36 holes to be played and a lot can happen. I just need to get a good round in (Saturday) and make a few putts."
Australia's Nick O'Hern (69) is alone in third place at 9-under 135.
Defending champion Henrik Stenson of Sweden (68) is tied for fourth with 1999 British Open champion Paul Lawrie (67) of England, Wen-Chong Liang (67) of China and Spain's Miguel Angel Jimenez (70) at 8-under 136.