The 21-year-old needed just 11 deliveries to go from 50 to 100, an Australian one-day domestic record, and needed just 11 more balls to bring up his hundred, including taking 32 runs off one over.
India's star-studded top four failed to fire against the West Indies, but Shikha Pandey's late show hauled them up to 107 and they defended it superbly, Poonam Yadav starring with the ball to earn a two-run win.
Agar ran around to attempt a straightforward catch at mid-on but slipped and copped the ball right between his eyes.
Shaun Marsh's name crops up as Australia look for right opening combo.
Defending champions Australia are grappling with injury concerns to three key players, including captain Aaron Finch who is uncertain to lead the side in their crucial T20 World Cup match against Afghanistan on Friday.
India finished third in the ICC Women's World Cup after Jhulan Goswami and her teammates edged past defending champions Australia by three wickets in a play-off match in Sydney on Saturday. The Indian bowlers ran through the Australian batting order, bundling the hosts for 142 in 44.4 overs. The Indians then faltered before eventually reaching 145 for seven wickets in 43.5 overs in the match reduced to 46-overs-a-side following rain.
Former captains, including Ian Chappell and Michael Clarke, have called for the inclusion of young opener Will Pucovski in Australia's team for the upcoming four-Test series against India.
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