The two players had seven birdies and two bogeys to total 16-under 200 at the Gary Player Country Club. Three-time champion Ernie Els (69) was next at 205, four strokes ahead of Henrik Stenson (72).
Immelman and Rose will play together for the second straight day Sunday.
'We can't let it become a match-play situation because it's a tough golf course, and there are some good players behind us that we have to keep our eyes on,' Immelman said.
Rose's bogeys were his first of the tournament, but he kept the pressure on Immelman with five birdies on the back nine.
Immelman pushed his drive on the 18th to the right, and his layup landed in a greenside bunker while Rose's second shot was just 12 feet short of the pin. Immelman's bunker shot left him only three feet from the hole to get away with just one dropped shot, while Rose missed his birdie attempt.
'Both times I felt I was faltering today, I managed to get three birdies in a row and get myself back in the tournament,' Rose said Rose.
Immelman was disappointed to start and finish his round with bogeys.
'There was a lot of good stuff in between, and I have just got to grind out each hole,' Immelman said.
Els had six birdies and three bogeys, achieving his the goal he set after the second round of scoring birdies on all four of the par-5s.
Rory Sabbatini (67) equaled the day's best round to move into seventh place at 5-under 211.
Two-time former U.S. Open champion Retief Goosen (75) continued his nightmare run in this year's event to be tied for last with Stewart Cink (75) in the 12-man field at 4-over 220.