After winning the toss and electing to bowl, stand-in skipper David Warner left England reeling at 3-34 in the fourth over when he ran out Dawid Malan with a brilliant direct hit.
The win ensured Australia will play in the tri-series final in Auckland, New Zealand, on February 21 with preliminary matches now switching to New Zealand.
Australia cruised to a seven-wicket victory over England with more than five overs to spare to remain unbeaten after three games in the triangular Twenty20 series in Melbourne on Saturday (February 10).
After Maxwell departed in the 14th over, Finch enjoyed an entertaining five-ball cameo that yielded a pair of sixes and two fours to complete the victory.
The injury could prove to be a major blow for England with team doctors yet to make a call on whether Morgan will be available for the New Zealand leg of the series.
England played without regular skipper Eoin Morgan, who strained his right groin during training and was replaced by James Vince.
This was an old-fashioned English limited-overs batting display before they adopted the spirit of adventure and positivity that has served them so well, particularly in the 50-over game.
"It was another poor performance from us", said Buttler.
Warner is the only member of the Test side to have played for Australia in every format this summer and has struggled for form in the ODIs and T20s.
The most fluent batting came from Sam Billings, something of a almost man in this England side, who hit 29 off 23 balls including one outrageous left-handed pull for four off Andrew Tye. An ideal opportunity to take global cricket to a venue where little is seen of the Australian team was missed.
Maxwell and Short combined for 39 off consecutive overs from Liam Dawson and Adil Rashid to end any hopes of an England comeback.
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