But South Africa, whose last International Cricket Council title came at the 1998 ICC Knockout, have such a long history of folding under pressure that their supporters will not be taking anything for granted against serial winners and WTC title-holders Australia.
Australia’s Mitchell Starc had starred earlier with bat and ball to put his team in charge. The tailender made 58 not out in Australia’s second-innings total of 207 and then, in his main role of left-arm fast bowler, dismissed Ryan Rickelton (six) and Wiaan Mulder (27) to leave the Proteas 70-2.
Starc almost had a third wicket when Bavuma got a thick edge only for Smith, in a helmet at an advanced slip position, to drop a fast-travelling catch and leave the field with a finger injury.
But with any early moisture in the surface long gone, conditions for batting at a sun-drenched Lord’s were now as good as at any time in the match.
Markram, aggressive from the outset, punched and pulled Australia captain Pat Cummins for well-struck fours.
With Australia appearing to miss absent former captain Smith’s tactical input, Bavuma produced the occasional gem of a shot, including a glorious drive down the ground off Cummins.
Australia spinner Nathan Lyon almost dismissed both batsmen, with Markram aiming a booming drive at a sharply turning off-break, only to miss the ball completely before it also beat wicketkeeper Alex Carey.
Bavuma had made 43 when a slog-sweep off Lyon evaded a diving Sam Konstas at deep midwicket as the substitute fielder attempted to pull off a low catch only for the ball to run away for four.
Soon afterwards, the diminutive Bavuma, who has a history of hamstring trouble, completed a gritty 83-ball 50.
Markram went to 97 with a brilliant straight-driven boundary off Josh Hazlewood and, shortly before stumps, clipped the fast bowler through midwicket to complete his hundred with an 11th four in 156 balls faced.
It was only the 30-year-old’s eighth hundred in 84 test innings.
Earlier Friday, South Africa enjoyed an early breakthrough when Kagiso Rabada had Nathan Lyon plumb lbw to leave Australia 148-9 in their second innings.
But tailender Starc, dropped in the gully on 14 by Marco Jansen late on day two, kept the Proteas at bay, ably assisted by Hazlewood, reaching the 11th half century of his 97-test career.
Part-time spinner Markram eventually succeeded where the frontline bowlers had failed when Hazlewood holed out to end a 59-run partnership for the last wicket.
Paceman Rabada took 4-59 to finish with nine wickets in the match.