The fun was South Africa slamming 174 runs in their last 90 balls, with Miller and du Plessis notching up big hundreds and giving their side 320 runs to defend.
But Marsh dug in with his WA teammate Stoinis, progressing steadily before they opened their shoulders in a fine 107-run stand.
But when he fell in the 42nd over, his side's chances virtually went with him.
It might have been ended in the 27th when Du Plessis, on 29, late cut Glenn Maxwell and wicketkeeper Alex Carey failed to latch onto the edge.
"It's always nice to score a hundred for your country".
However, he did know that he had one of the biggest hitters in world cricket at the other end - David Miller. "We needed one more batter to stay with Dave".
Du Plessis, who had saved his front-line bowlers - Rabada, Ngidi and Steyn - for the death, unleashed them from the 44th over onwards, but Maxwell, undeterred, smashed Rabada for a boundary through mid-wicket to bring it down to 71 off 36. The previous highest partnership against Australia was a 237-run stand between Marvan Atapattu and Sanath Jayasuriya in an ODI in 2003.
Du Plessis and Miller together scored 130 from the last 10 overs and 75 of them came in the last five overs.
Thereafter began the counter-attack from captain Faf du Plessis (125) and David Miller (139), who added 252 runs for the fourth wicket and helped South Africa post a solid total.
Ball-tracking was to show the ball hitting in line but bouncing fractionally over the leg stump, meaning a reprieve on 41 for Miller, and more than a few befuddled Australian faces.
"I thought the way we set up the game was really good". While captain Aaron Finch had said before the match that off-field issues may have been causing "doubts" among his side, Hazlewood felt the opposite was the case and they were just making sure they concentrated on getting it right on the field.
A brilliant Shaun Marsh century and a brutal 63 from Marcus Stoinis weren't enough to get Australia home in the one-day series decider at Blundstone Arena. "Then obviously it went upstairs".
"With Dave it is about understanding his blueprint of how to score runs", said du Plessis.
"It's been a tough six months so just really happy that we can chill out now, at least for a day and then get into the next game".
All-rounder Marcus Stoinis took three wickets to fire Australia to a seven-run win over South Africa at the Adelaide Oval on Friday, ending the hosts' record seven-match losing streak and levelling the three-match one-day global series.
Their chase started disastrously, losing Chris Lynn to a first-ball duck before Aaron Finch (11) and Travis Head (6) joined him.