They dominated India in all three departments even though the tournament co-hosts did not last a full 50 overs in what was possibly the only blemish in their 106-run win.
Left-handed Warner (104) played his natural game, racing to his century in 80 balls.
Maxwell (122) did even better, needing 53 balls to reach the 100-mark, his second 50 coming in just 19 balls.
There was momentary discomfort for Maxwell, whose attempted hook off Umesh Yadav resulted in an inside edge that crashed onto his helmet and he also needed medical attention on his lower back after reaching 50.
Maxwell retired to allow his team mates to get some batting practice but not before plundering 27 runs from a Yadav over and hitting three sixes in a row.
India, having lost paceman Ishant Sharma to a knee injury earlier in the day, had a scare when Mohammad Shami (3-83) left the field with a split webbing but returned soon after to resume bowling.
Their batting on a good track could not offer much relief, however, with only Shikhar Dhawan (59), Ajinkya Rahane (66) and Ambati Rayudu (53) managing to impress.
Batting mainstay Virat Kohli dragged a Mitchell Starc delivery onto his stumps and the Australian nonchalantly took a one-handed blinder on the edge of the boundary to dismiss India captain Mahendra Singh Dhoni for a golden duck.
"It was a very good performance," said Australia stand-in skipper George Bailey before pointing out areas his team could still improve.
"Early wickets tonight would have been nice, just to blow the game out of the water. As great as our batting was, we were probably one wicket down too many and you'd like to see Mitchell Starc catch with both hands," he quipped.
Dhoni said he was still looking for the final 11 players for next Sunday's tournament opener against Pakistan.
"It's a very long tournament and what we have seen is the team that does well is the one that comes from the bottom and slowly picks up momentum," he added.
(Reporting by Amlan Chakraborty in New Delhi, editing by Alan Baldwin)
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