The tournament, being contested at the Gary Player County Club, features an invited field of 12 top golfers.
Rose, who won the 2007 European Tour Order of Merit, and Immelman are tied at 11-under 133 after 36 holes, three shots ahead of Ernie Els, who shot 67 Friday and is at 8-under for the tournament. Henrik Stenson was fourth at 7-under while Adam Scott, who was tied with Immelman for the first-round lead, was in fifth at 6-under.
Luke Donald was in sixth at 5-under while Geoff Ogilvy was at 2-under 142 and in seventh place. Rory Sabbatini (144) was eighth and Stewart Cink and Retief Goosen shared ninth at 1-over 145. Niclas Fasth (146) and Charl Schwartzel (148) complete the field.
Rose played his second nine in 5-under, including posting birdies on three of the first four holes of the side. It was his birdie on the 18th hole and pulled him into the tie for the lead.
Immelman had three birdies in the last four holes of his first nine Friday and finished with three birdies and a bogey in his final five holes.