On a day when Inglis brought up his second Test ton before being dismissed for 102, Cooper Connolly took Australia to a three-figure lead after lunch in Cape Town.
The West Australian finished with 29 before being caught-and-bowled by Marco Jansen, after taking charge of the innings when his side lost 3-10 on Thursday morning.
The extra 49 runs from that point could prove crucial in the third Test, with the pitch showing signs of turn and spinner Simon Harmer taking 4-107.
Inglis enjoyed the most important innings of his career after being called in late to replace Steve Smith, bringing up his ton when he reverse-swept Harmer to the boundary.
At that point the Proteas had started the day reasonably flat, with a number of misfields at Newlands under the warm Cape Town sun.
But when he was caught behind later in the same over and a 185-run stand with Alex Carey was ended, the Proteas were suddenly back in the contest.
Carey edged Harmer to slip four overs later on 80, before Pat Cummins was trapped lbw by Kagiso Rabada in the mini collapse.
But Connolly showed a glimpse of why he is so highly rated, building Australia's total alongside Mitchell Starc (11) and Nathan Lyon (1).
Playing in just his second Test, the No.7 flayed one ball away over backward point for four off Gerald Coetzee.
The shot of the day also came off the right armer, when he drove a low full toss for four through the covers shortly before the break.
He played a similar shot from Jansen (3-60) after lunch, to a ball that wasn't all that full.
His runs came after Inglis had resumed at 85 on Thursday morning and showed no sign of nerves on his way to another century to accompany his debut ton last year in Sri Lanka.
Inglis's runs came after he would have likely featured earlier in the series, if not for a fractured finger.
While Matt Renshaw (74) and Cameron Green (65) did the grunt work for Australia on Wednesday, Inglis and Carey played a vital role in giving Australia the advantage.
After Renshaw and Green's dismissals in quick succession left Australia 4-185 in reply to the Proteas' 329 before tea on Wednesday, the pair of glovemen steadied the ship.
Inglis was patient through the early stages of his innings on Wednesday, before going through the gears nicely as he swept and cut well.
The century made Inglis the first Australian male to have multiple hundreds in all three formats, having previously made his name in the white-ball game.
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