The American shot 3-under 69 at the Gary Player Country Club to move to 7-under par for the tournament.
He trails overnight leader Darren Clarke by a shot; however, Clarke is among the 61 players who will have to continue their second rounds on Saturday.
The Northern Irishman is 1-over on the day through nine holes at the Gary Player Country Club, and 8-under overall.
Trevor Immelman is tied with Dunlap at 7-under, but has 12 holes remaining in his second round.
Rain and lightning delayed the start of play Friday by four-and-a-half hours in Sun City, South Africa.
Dunlap, who won this event in 1999, was one of the lucky ones to finish. He made five birdies and dropped only two shots on the soggy venue, which will be the primary host over the final two rounds.
Its great to come back to places where youve done well, and you just seem to put it on autopilot, he said. You know where to aim and how its going to play. Today, the wind blew more than Ive ever seen it here which was a little more of a challenge.
Players alternated between the Gary Player course and the Lost City course over the first two days. Of those playing the Lost City course on Day 2, South Africans Titch Moore (68) and Mark Murless (71), and American Bruce Vaughn (68) have the lowest total, at 4-under. All three completed their second rounds.