Pakistan were put into bat by the Aussies and reached 191-5 from their 20 overs.
They were led by Umar Akmal, who scored 94 off 54 balls with 13 boundaries before he lost his wicket in the final over.
The pair took Australia's total way past 100 before Maxwell's impressive innings, in which he smacked six sixes, ended on 74 off just 33 balls.
Finch reached 65 before he was bowled by Saeed Ajmal, with no other Australian batsman getting into double figures as their tail end collapsed.
Next up for Australia is a match against the West Indies on Friday. Meanwhile, Pakistan have a week until their next match when they face hosts Bangladesh.