- Tag results for Australia Vs England
Finch was involved as England completed their first 5-0 sweep of Australia in any format in more than 140 years of men's cricket between the arch-rivals.
England, India and South Africa currently occupy the top three spots in the ICC One-Day International rankings.
England all-rounder Ben Stokes and paceman Chris Woakes will miss the remainder of the ODI series with Australia.
Maxwell was twice dismissed in single figures by spinners during Australia's warm-up matches against Sussex and Middlesex.
Ben Stokes has revealed his pain at missing England's Ashes campaign after being sidelined over an alleged fight outside a nightclub.
England were reeling at 34 for three in the fourth over when David Warner ran out Dawid Malan with a brilliant direct hit.
Maxwell hit a six from Mark Wood's bowling with the scores tied to go from 97 to 103 and to carry Australia to 161-5 in reply to England's 155-9.
Buttler also shared an unbroken partnership of 113 runs with Chris Woakes for the seventh wicket to rebuild England's innings after the tourists had slumped to 189-6 in the 39th over.
England retained the same team that beat Australia by five wickets in Melbourne and then four wickets in Brisbane.
Finch blasted 106 from 114 balls, including nine fours and a six, to follow the 107 he made at the MCG on Sunday.
Australia have made three changes from the team that lost to England in Melbourne on Sunday including two debutants.
Finch's century was backed by fifties from Mitchell Marsh and Marcus Stoinis as Australia recovered from a shaky start as England got bogeyman Steve Smith cheaply.
Usman Khawaja batted for nearly nine hours over two days in amassing his 171, just missing his highest test score of 175.
The left-hander was unconquered on 166 off 368 balls and just off his highest Test innings of 174 scored against New Zealand in Brisbane in 2015.
At lunch, Australia were 277 for three and trailing the tourists by 69 runs with Khawaja unbeaten on 132 and Shaun Marsh not out two.