Warner, who was seeking redemption after his reckless dismissal in the opening over of the first innings, lost his wicket while at the forefront of Australia's fightback.
At stumps on the third day the home side were hanging in at 121 for two, still 120 runs behind the Proteas, who have been in control of the Test since routing Australia for 85 on Saturday.
Usman Khawaja was unbeaten on 56, his ninth Test half-century, with skipper Steve Smith not out 18.
It gave the Proteas a huge fillip after Warner and Khawaja had recovered the innings with a 79-run stand after the loss of Joe Burns in the first over.
Burns lasted just four balls before he was caught behind, tickling at one wide down the leg-side from Abbott.
Lightning had struck twice for Australia with fellow opener Warner out to an expansive shot in the opening over in the first innings of the Test.
- De Kock century -
===================
Australia face a mighty struggle to prevent South Africa, already 1-0 up, from claiming their third successive series in Australia with only next week's day-night third Test in Adelaide still to play.
South Africa earlier extended their first innings lead to 241 before they were all out for 326 with Quinton de Kock plundering a century and Josh Hazlewood finishing with six for 89.
Hazlewood captured three of the last four wickets to fall after lunch for his second best haul after his six for 70 against New Zealand in Adelaide last year to take his tally to 88 Test wickets.
Keshav Maharaj followed shortly after, bowled by Hazlewood for one and Abbott lasted nine balls before he became the speedster's fifth dismissal for three.
Vernon Philander was the last man out for 32 off 28 balls, caught behind off Hazlewood.
After Sunday's second day was washed out, the Australians chased early wickets but de Kock and Bavuma batted South Africa into a position of strength with a century stand.
His stand of 144 with Bavuma was the highest by a visiting team in Hobart for the sixth wicket.
De Kock became only the fourth South African to register 50 or more in five consecutive Tests after he swept spinner Nathan Lyon for four over wide mid-on.
He has proven a thorn for Australia in this series following scores of 84 and 64 in the first Test victory in Perth.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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