Fresh off taking 37 wickets in Australia's Ashes demolition of England, Johnson (4-51 off 13.3 overs) picked up where he left off with another superb exhibition of hostile bowling on Thursday.
South Africa bowled well to reduce the tourists – who resumed at 4-297 – to 397 all out despite Steve Smith (100) reaching his century and Shaun Marsh pushing to 148.
But their good work was undone by a poor display from their top-order as Graeme Smith (10), Alviro Petersen (2), Faf du Plessis (3) and Hashim Amla (17) all failed, with only AB de Villiers (52 not out) offering resistance.
Johnson's heroics were not limited to his efforts with the ball – he also took a stunning catch to dismiss JP Duminy (25) off the bowling of Nathan Lyon (1-23 off 11) at a crucial time.
Peter Siddle (1-21 off seven) was Australia's other wicket-taker while Ryan Harris (0-33 off 12) bowled well without luck.
The Proteas were on the back foot as early as the second over as Smith failed to get out of the way of a sharp Johnson bouncer, ballooning a catch to Shaun Marsh at first slip, and the left-armer struck again in the sixth over as Petersen edged a loose drive to wicket-keeper Brad Haddin.
Another short ball from Johnson undid Du Plessis, who was caught by Michael Clarke at second slip, and a late inswinger from Siddle saw Amla given out lbw on a referral.
De Villiers and Duminy steadied the ship, adding 67 for the fifth wicket, but the latter misjudged the flight of a Lyon delivery and skied to a diving Johnson.
The left-armer still had time to bowl Ryan McLaren for eight before the rain intervened, leaving De Villiers and Robin Peterson (10 not out) at the crease at stumps.
Earlier in the day, Smith scored his third century in his last four Tests, only to fall in the very next over when he edged McLaren (2-72 off 20) to Petersen at second slip.
A 43-run stand between Johnson (33) and Harris (19) frustrated the hosts after Marsh fell, caught at first slip off Vernon Philander (1-69 off 24), but Australia could only add six runs for the final three wickets as Dale Steyn (4-78 off 29) finished well.
All eyes will be on De Villiers, who came into the series on the back of good form against India, to get South Africa to a competitive score when play resumes on Friday.