Johnson hammered 123 not out but it was in a losing cause, as Australia were bowled out for 422, shortly before the scheduled close on the fourth day.
Australia had already clinched the series by winning the first two tests.
"Obviously, any time you lose it really hurts, but this has been really poor," Ponting told a news conference after Australia were condemned to their first innings defeat since India beat them in Calcutta in 1998.
"The first two tests were as good as we have played, while the first two days here were as bad as we have ever played. It shows if you're not quite there in terms of your best then results are not going to go your way."
Left-arm spinner Paul Harris was South Africa's hero with the ball, taking six for 127.
South Africa had scored 651 in their first innings, in reply to Australia's 209.
The Newlands pitch remained wonderful for batting and Johnson and Andrew McDonald used the final session to post a seventh-wicket stand of 163 off just 161 balls.
Johnson clobbered 11 fours and five sixes and reached his century half an hour before the end.
Harris claimed three wickets in the final session after McDonald and Johnson had threatened to take the match into the final day.
Harris eventually killed off the innings by having McDonald, who scored a career-best 68, and Peter Siddle caught at silly point by AB de Villiers off successive deliveries, then having Ben Hilfenhaus caught at slip for 12.
South African stand-in captain Jacques Kallis said the triumph had provided the team with a major boost before their next test series.
