Sent into bat, Australia rode Finch's 128-ball 135 and Maxwell's enterprising knock to lay the foundation for a big score at the Melbourne Cricket Ground.
Finch hit 12 boundaries and three sixes while the big-hitting Maxwell found the fence 11 times.
Skipper George Bailey also made substantial contribution, scoring 55 off 69 balls while sharing a 146-run stand for the fourth wicket.
Leading the co-hosts in the absence of Michael Clarke, Bailey's innings was laced with three hits to fence.
For three-times runner-up England, seeking to script their maiden ODI World Cup title, seamer Steven Finn was the most successful bowler, returning figures of 5/71, while Stuart Broad took two wickets.
Finch felt the love of his home crowd as the Victorian marked Valentine's Day with the first hundred of the tournament.
Finch, dropped on nought by Chris Woakes off James Anderson, helped Australia off to a blistering start before Broad pulled England back into the match with two wickets in two balls to remove David Warner (22) and Shane Watson (0).
Finch's innings ended when he was run out by England captain Eoin Morgan's direct hit from mid-off while going for a needless single. Bailey followed soon afterwards, playing on to Finn.
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