Chasing 348 to win, the Bushrangers survived a perilous final session at the MCG to finish on 8-273.
The Redbacks were well in control and pressed for victory but Peter Siddle (14 not out) and Scott Boland (six not out) survived the new ball as the Redbacks search for their first win of the season.
Jake Lehmann was named player of the match for his 103 and 93 which steered the Redbacks to two competitive totals alongside Callum Ferguson.
The veteran batsman scored a brilliant 182 not out in his 100th Sheffield Shield match as the Redbacks declared on 8-370 in the second innings.
Maxwell and Test teammate Peter Handscomb (58) combined for a 104-run partnership as the Bushrangers went to tea at 3-157 in reply.
Handscomb fell soon after to a brilliant Chadd Sayers catch at mid-on off the bowling of Adam Zampa.
Aaron Finch (54) and Daniel Christian (38) looked to push the run rate but were each undone by their own aggression.
Tall paceman Mennie (4-39) was the pick of South Australia's bowlers while Sayers claimed a tidy 1-39.
The Redbacks next face Western Australia in Perth on Monday, 13 November.
Meanwhile, also in Melbourne, SA’s Toyota Futures League side has a battle ahead to save the game against Victoria.
The Redbacks were dismissed for 192 in their first innings, 206 runs behind Victoria at Shepley Oval in Melbourne. Jake Walker top-scored for SA with 56.
Victoria was 2/53 at stumps on day two.