Australia face a mighty struggle to prevent South Africa from claiming their third successive series in Australia.
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 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.
Warner flung his head back in despair when a ball from Kyle Abbott hit his hip and ricocheted off an elbow onto his stumps when he was on 45.
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.
"We've done well with the bat, two unlucky dismissals, but that happens in cricket and the boys have shown some good fight, digging in even though the ball is nipping around a fair bit," Australian paceman Josh Hazlewood said.
"A really good partnership in the morning, a good first hour and that will go a long way to having a good day tomorrow."
Khawaja played some lovely shots in his vigil, providing great support for his captain Smith, who top scored with an unbeaten 48 in the first innings shambles.
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 Hazlewood finishing with six for 89.
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.
The swashbuckling wicketkeeper, likened to Australian Test great Adam Gilchrist, was bowled by Hazlewood just before lunch for 104 off 143 balls with 17 boundaries.
His stand of 144 with Bavuma was the highest by a visiting team in Hobart for the sixth wicket.
"Obviously, I'm happy with what we've done and what we've achieved, but the game has only gone past halfway and we still have a lot to do," de Kock said.
"The Aussies looked very determined in their second innings so we have a lot to play for."
De Kock has scored 540 runs in 2016 in just nine Test innings and leads the year's international averages with 80 having been unbeaten twice.
He 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.
Shortly after lunch, Tembo Bavuma was surprised by a rearing delivery to spoon an easy catch to Nathan Lyon at point and give Joe Mennie his first Test wicket for 74.
Vernon Philander was the last man out for 32 off 28 balls, caught behind off Hazlewood.