Shaheen Afridi took out three Australia top-order batsmen as Pakistan won its last round-robin match in the T20 tri-series by 45 runs on Thursday.
Earlier, opening batsman Fakhar Zaman maintained a brilliant run of form by scoring 73 off 42 deliveries and Asif Ali hit a rapid 37 off 18 balls to provide Pakistan with an imposing total of 194-7.
Both teams have already qualified for Sunday's final.
Australia, which defeated Pakistan by nine wickets on Monday, will take on Zimbabwe in a dead rubber on Friday, having beaten the host by 100 runs earlier.
"Afridi has been part of the last two, three series, so we wanted to give him an opportunity. Glad he did well," Pakistan captain Sarfraz Ahmed said.
"Fakhar, too, he was superb. Today's surface wasn't the easiest."
Finch couldn't have asked for a better start after he won the toss and elected to field when Jhye Richardson dismissed Haris Sohail off his very first delivery.
But the Australians were sloppy in the field as Marcus Stoinis dropped Hussain Talat on 9 at mid-off which could have reduced Pakistan to 19-2.
Talat went on to score 30 and contributed to a 72-run stand with Zaman for the second wicket before he was bowled by offspinner Maxwell.
Zaman then took charge and hammered nine fours and three sixes before he mistimed a pull shot of seamer Stoinis and was caught at mid-wicket.
Asif and Malik (27 off 15 balls) then propelled Pakistan in the last five overs which yielded 60 runs despite Andrew Tye finishing with 3-35.
"We didn't get going all day, long way off with the ball and on the field, couldn't then get any partnerships with the bat," Finch said.
"This was a 170 wicket, we let them get away, our fielding was sloppy as well. They stuck to basic plans and did well."
Afridi, who impressed in this year's Under-19 World Cup, struck three blows upfront that took the game away from Australia.
Finch, who scored a world-record 172 against Zimbabwe and a rapid half-century against Pakistan in the first game, tried to play across the line and was caught behind for 16.
Maxwell fell lbw to a superb Afridi in-swinger on 10, and Short's struggling 28-run knock off 34 balls ended in the 13th over when he was clean bowled by Afridi.
Alex Carey top-scored with 37 to reduce the margin of defeat, but Australia couldn't recover after losing half of its side for 75 runs when Short departed.