Bailey (98) and Maxwell (92) were the main contributors for Australia as the tourists set India a total of 8-295 from their 50 overs in Ranchi.
However, the inclement weather denied India the chance to mount a response as play was abandoned with the hosts 0-27 in reply.
Australia made a shaky start to their innings - which was interrupted by rain - as Aaron Finch (5), Phillip Hughes (11) and Shane Watson (14) all went cheaply off the bowling of Mohammed Shami (3-42) to fall to 3-32 inside the first eight overs.
Bailey was dropped by Virat Kohli on the first ball of his innings after Shami had dismissed Hughes, and it looked as if it would prove to be a costly mistake.
Adam Voges (7) was accounted for by Ravichandran Ashwin (2-57) as Australia slipped to 71-4, but Bailey and Maxwell mounted an excellent recovery with a fifth-wicket partnership of 153.
Bailey was denied a century, though, as he top-edged a short delivery from Vinay Kumar (2-52) into the hands of Rohit Sharma to leave his side on 5-224.
The wickets quickly began to tumble following Bailey's exit, wicket-keeper Brad Haddin (3) bowled by Ravindra Jadeja (1-56), before Maxwell fell eight runs shy of his hundred as he was trapped lbw by Kumar.
There was some late resistance from the lower order, however, with James Faulkner (23 not out) and Mitchell Johnson (25), helping Australia to a relatively imposing score.
Sharma (9 not out) and Shikhar Dhawan (14 not out) looked to be setting the hosts up for a strong reply, but the rain soon arrived to end any hopes of a result.
The washout leaves the seven-match series finely poised with Australia holding a 2-1 advantage ahead of their fifth ODI in Cuttack on Saturday.