Australia bowled out South Africa for 287, a lead of 207, and added another 27 runs for no wicket before close of play.
Harris took three for 63 and Johnson four for 42.
Captain Michael Clarke's decision to declare at Australia's overnight total of 494 for seven paid off as his South African counterpart Graeme Smith failed again and South Africa lost four wickets before lunch.
Despite losing early wickets, South Africa scored freely during an extended morning's play, reaching 127 for four off 32 overs at lunch.
JP Duminy fell to a catch behind by Brad Haddin off Harris for four before Faf du Plessis and Vernon Philander came together in a seventh-wicket stand of 95, the best of the innings.
Du Plessis battled his way to 67 before Johnson returned to the attack and he edged a drive fast and low to gully, where David Warner held a good catch.
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