Allrounder Maxwell limped off with a suspected low-grade issue in Hobart on Monday night after pulling up sore while fielding.
He wasn't required to bat and will have almost a month to recover for the Melbourne Stars' Big Bash League season opener against Perth on December 15.
After losing the toss, Australia skittled Pakistan for 117 in the penultimate over before ironing out the chase with more than eight overs to spare.
Stoinis was slow to get going before whacking five fours and five sixes, including one which reached the roof of the members stand at Ninja Stadium, in an unbeaten 61 off 27 balls.
It was Australia's first clean sweep of a T20 series against Pakistan.
Nathan Ellis was among five Australian bowlers to take wickets in an all-round team performance. (Linda Higginson/AAP PHOTOS)
Earlier, Aaron Hardie's career-best white ball figures of 3-21 and Adam Zampa's ultra economical 2-11 ripped the heart out of the Pakistan innings.
The tourists, who rested skipper and wicketkeeper Mohammad Rizwan and quick Naseem Shah, got off to a promising start and were 1-61 in the seventh over.
But it fell away quickly in a horror collapse of 6-31 through the middle overs.
Babar Azam (41 from 28) top scored but couldn't hold his nerve and was bowled trying to hit Zampa in the 13th over.
It came after a tumultuous 24 hours for Pakistan, who were forced to refute a report that red ball coach and interim white ball coach Jason Gillespie had been sacked.
Salman Agha was trapped lbw as one of three wickets for Aaron Hardie. (Linda Higginson/AAP PHOTOS)
Australia lost openers Matthew Short (two) and Jake Fraser-McGurk (18) inside the first four overs of the chase before skipper Josh Inglis (27) steadied the ship.
After picking up the best T20I figures by an Australian quick at the SCG on Saturday, Spencer Johnson took 2-24 and ended the Pakistan innings by bowling Sufiyan Muqeem.
Johnson topped the series wicket tally with eight.
Fans were left queuing for tickets after the match had started. (Ethan James/AAP PHOTOS)
There were lengthy queues for tickets outside the ground after the match had started following an issue with the Ticketek website.
Australia claimed the first two games of the series in Brisbane and Sydney.
Attention now turns to the first Test of the summer against India on Friday.
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