David Warner, on 29, and Usman Khawaja (24 not out) steadied for the hosts after Burns' dismissal, with Australia moving to 54 for one at the break at Bellerive Oval.
On a day punctuated by rain squalls, South Africa were bowled out for 326 after lunch in response to Australia's paltry 85.
Wicketkeeper-batsman Quinton de Kock scored a sparkling 104 to propel the tourists to a commanding 241-run lead.
Burns, trapped lbw by Abbott for one run in the first innings, lasted four balls before nicking behind to De Kock in the first over.
Warner dodged a huge bullet in the final over of the session when slips fielder JP Duminy inexplicably ducked rather than attempt to catch an edge off the left-hander off Abbott's bowling. Warner was on 24 at the time.
De Kock earlier raised his second Test century in a decisive 144-run stand with Temba Bavuma before being bowled by Josh Hazlewood just before lunch.
Hazlewood finished with 6-89.
Having piled on 117 runs for the loss of one batsman in the morning, the Proteas lost their final four wickets for 50.
Australia debutant Joe Mennie captured his maiden test wicket when Bavuma miscued a pull to Nathan Lyon at point and was out for 74 shortly after lunch.
Hazlewood bowled Keshav Maharaj for one and had Abbott lbw for three.
The paceman wrapped up the innings by having Vernon Philander caught behind for a quickfire 32.
Rain washed out day two, leaving De Kock and Bavuma to resume in the morning on 171-5.
Australia's seamers laboured with the ageing ball and the pair were rarely tested in the first session.
Untroubled by front-line pacemen Mitchell Starc and Hazlewood, the pair hammered Lyon, with De Kock raising his fifth half-century from five innings with a contemptuous slog off the spinner's second ball.
De Kock was reprieved on 72 when wicketkeeper Peter Nevill missed a stumping chance off Lyon.
De Kock hammered Mennie off his pads to the fence past midwicket to reach 99 with his 16th four and poked a single square to raise his ton.
South Africa won the series-opener in Perth by 177 runs.
ReutersSouth Africa paceman Kyle Abbott struck an early blow by dismissing Australia opener Joe Burns for a duck as the home side battled to haul in a first-innings deficit of 187 at tea on day three of the second Test.
Original source: Aussies recover after early wicket