The Proteas came into the fifth and final day at Kingsmead on 102-4, still 319 runs shy of an improbable target of 421, but looking to bat time and maybe a force a draw in the opening Test of the three-match series.
Markram resumed on 45 while Wiaan Mulder was with the opener on 5, and the duo battled for the first hour, taking their partnership to 69 while consuming 205 deliveries.
Australia made the breakthrough when Hazelwood had Mulder caught down the leg-side, wicketkeeper Alex Carey taking a smart catch diving to his left and clutching the ball with one glove.
The Proteas allrounder was visibly disappointed as he trudged back to the dressing room after batting for 110 balls for his 25, but it was the start of the end as Kyle Verreynne was caught at slip off the part-time bowling of Matt Renshaw, who claimed his second Test wicket.
Markram and Marco Jansen took the Proteas to lunch at 166-6 and the latter struck six fours and a six after the interval to go to 35 before being clean bowled by Hazlewood.
The evergreen seamer then had Simon Harmer caught behind to complete his five-wicket haul before Mitchell Starc finally got rid of Markram, who absorbed 237 balls and 358 minutes at the crease for his 75.
Hazlewood then fittingly ended the contest when he dismissed last man Anrich Nortje to finish with Test best figures of 6-49 in 16.5 overs.
The Proteas will have to dust themselves off quickly if they want to come back into the series with the second Test starting at St George's Park in Gqeberha on Sunday.
Temba Bavuma suffered his first defeat as Test captain after the Proteas went down by 214 runs against Australia in Durban, and the home skipper could not hide his disappointment.
The Proteas will face a battle on the final day to save the opening Test against Australia in Durban, going to stumps on 102-4 after being set a target of 421.
Australia have earned a 139-run lead over South Africa after bowling out the lacklustre hosts for 284 runs in their first innings at Kingsmead Stadium on Sunday.
Australia will welcome Josh Inglis back into their squad ahead of the second Test against South Africa as the wicketkeeper-batter continues his recovery from a fractured finger.
