Burns lasted just four balls before he was caught behind, tickling at one down the leg-side from Kyle Abbott.
Lightning had struck twice for Australia with fellow opener David Warner out to a reckless shot in the opening over in the first innings of the Hobart Test.
But Warner was a different proposition on the easier batting conditions the second time around and scored freely with Usman Khawaja in support.
At tea, the home side were 54 for one, still trailing by 187, with Warner on 29 and Khawaja on 24.
More From This Section
South Africa earlier extended their first innings lead to 241 runs before they were all out for 326 with Josh Hazlewood finishing with six for 89 off 30.5 overs.
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.
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.
Keshav Maharaj followed shortly after, bowled by Hazlewood for one and Kyke 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 before the swashbuckling wicketkeeper was bowled by Hazlewood just before lunch for 104 off 143 balls with 17 boundaries.
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.