The right-hander was perfectly placed to become the 11th batsman in the world — and first from Australia — to reach three figures in three consecutive ODI innings.
Virat Kohli and AB de Villiers are among the luminaries on that list headed by Sri Lanka great Kumar Sangakkara, who is the only batsman to have scored four ODI tons in a row.
But Finch was unable to join the exclusive club and fell victim to Yasir Shah, the veteran spinner he has tormented for much of the series.
The hard-hitting opener, who generally shelved his natural aggression during the 136-ball innings, picked out Haris Sohail in the deep during the 42nd over.
Maxwell, who was dropped on 27, then overwhelmed Pakistan with a mix of audacious strokes, assertive running between the wickets and nine boundaries.
Finch led from the front again, backing up match-winning knocks of 116 and 153 not out, the highest score of his ODI career.
The Victorian scored 14 runs from his first 32 balls as Australia slipped to 2-20 but launched a powerful six back over the head of Shah to find some rhythm.
Finch reached 50 in 82 deliveries.
Only once before, during Australia’s 2015 World Cup semi-final against India at the SCG, has Finch taken so long to make an ODI half-century.
The skipper ensured there was no repeat of the sort of collapse that has been a hallmark of Australia’s recent barren years, steadying after Marcus Stoinis and Peter Handscomb were clean bowled in contrasting fashion.
Usman Shinwari spearheaded a testing new-ball examination and started the match with a wicket maiden, working over Usman Khawaja in textbook fashion to dismiss the in-form opener for a duck.
Australia are seeking to win the series and bank a sixth straight one-day win for the first time since a 2015 streak, which included the World Cup final.