Elgar’s 109 at the Allan Border Field came off 186 balls and included nine fours.
Kyle Verreynne ended the day unbeaten on 76 off 86 deliveries, having hit 13 fours and a six, as the Proteas posted 335-7 in 90 overs.
Keshav Maharaj was the next highest-scorer with 34, followed by Rassie van der Dussen (27), Sarel Erwee (25), Khaya Zondo (18) and Theunis de Bruyn (13).
Temba Bavuma did not bat due to discomfort in his left elbow, but is expected to do so in the second innings.
Matthew Kuhnemann took 4-78 with the ball for the hosts.
WATCH: Runs on the board vital in Oz – Elgar
The match does not have first-class status, allowing all Proteas squad members to get game time.
The first Test between Australia and South Africa at the Gabba in Brisbane starts on 17 December.
