The 30-year-old notched his 16th century and also passed 5,000 test runs.
Aussie pacers made ideal use of the new ball to get rid of KL Rahul, Murali Vijay and Virat Kohli inside the first 11 overs with Mitchell Starc, Josh Hazlewood and Pat Cummins striking once each. The Saurashtra right-hander has given the blueprint for the rest of the batsmen to follow after another poor show by the top order after Virat Kohli won the toss and chose to bat. He found willing support through Ravichandran Ashwin (25) as the pair combined for a 62-run seventh wicket partnership.
Virat Kohli was dismissed for just three by a sensational catch from Usman Khawaja, before Cheteshwar Pujara struck a defiant century in an Adelaide Oval furnace to rescue India. Australia's four-pronged attack shared the spoils with two wickets apiece.
Aided by a hint of bounce and movement, Australia's trio of quick bowlers did all the damage in a fiery opening session before Nathan Lyon took over after lunch.
Marsh's place in the side for the series-opener, which starts on Thursday, has been taken by middle order batsman Peter Handscomb, recalled for the first time since the tour of South Africa in March and April.
The experienced number three did what he has done many times before and stood his ground as wickets tumbled around him, including superstar Virat Kohli for three, with India stumbling to 143-6 at tea on day one.
Khawaja dived and snared the ball in his left hand.
Ajinkya Rahane (13) fell in the slips to an impulsive stroke as India crashed to 56-4 at lunch.
When Lyon stuck to the same channels, Rohit went after him with another ugly slog sweep - a ball after the six - and top-edged down the throat of the fielder.
Out of the final 12 picked on the eve of the game, Rohit Sharma made the cut in the Indian playing eleven ahead of Hanuma Vihari.
A crowd of 23,802 braved the heat but the figure was considerably less than previous opening days for the Adelaide day-night tests.
Initially, Pujara was circumspect as India stumbled to 6-127 - his first 50 runs came from 153 balls.