Warner was out for 63 as South Africa came back with five wickets in the afternoon following a solid opening session for the tourists.
Fast bowler Kagiso Rabada was responsible for that big comeback, taking three wickets in the space of two overs just before tea.
Rabada also may have further stoked the lingering animosity between the teams after appearing to intentionally bump into Steve Smith in his follow-through after dismissing the Australia captain.
Bancroft fell on the brink of lunch for 38. Usman Khawaja (4), Warner, Smith (25), Shaun Marsh (24) and Mitchell Marsh (4) were out after lunch to turn the tide in South Africa's favor.
Rabada returned 3-67 with that deadly late spell and Vernon Philander had 2-13.
Australia vice-captain Warner was the centre of attention in the series opener in Durban after his ugly confrontation with South Africa wicketkeeper Quinton de Kock on a staircase leading to the teams' dressing rooms. Both received fines and disciplinary sanctions from the International Cricket Council. Australia won by 118 runs for an early lead in the four-test series.
They picked off the runs after that measured start, with Warner accelerating by hitting nine fours.
South Africa made an important breakthrough when Warner, who looked in good touch, was bowled by Lungi Ngidi to follow Khawaja back to the dressing rooms after lunch.
Smith and Shaun Marsh put on 44 before Rabada roared back late in the second session.
Rabada took those three wickets in the space of six balls.
The atmosphere was subdued at the start of the second test but the fallout from Durban and the Warner-de Kock affair continued, with Cricket Australia chief executive James Sutherland releasing a statement before play started reminding the Australian players they needed to behave. Match referee Jeff Crowe also called the captains and managers to a meeting on the eve of the test in an attempt to calm the situation.
For Port Elizabeth, Australia retained the same team that won in Durban while South Africa made one change, bringing in fast bowler Lungi Ngidi for Morne Morkel.
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