Australia will take on New Zealand in the final on Sunday after the Black Caps defeated England in the first semi-final.
Australia have reached the Twenty20 World Cup final with a five-wicket victory over Pakistan in the second semi-final.
Chasing 177 for victory, David Warner made 49 before Australia were in trouble at 96-5 when Stoinis (40) and Wade, who hit three successive sixes in his 41, put on 81 to finish off the match with one over to spare on Thursday.
Earlier, Mohammad Rizwan and Fakhar Zaman smashed breezy half-centuries to help Pakistan post 176-4 at the Dubai International Stadium.
Put in to bat, Pakistan got off to a strong start with Rizwan (67) and skipper Babar Azam (39) forging a 71-run partnership for the opening wicket.
Fakhar provided the late charge for the 2009 champions with an unbeaten 55 off 32 balls.
Afridi's left-arm swing has troubled the best in the tournament and Finch became his latest victim when Australia began their chase.
Afridi trapped Finch lbw for a duck to give Pakistan a dream start with the ball.
David Warner (49) and Mitchell Marsh (28) survived Afridi's searing spell to rebuild the innings before Shadab Khan (4-26) ripped the heart out of Australia's top order.
Australia will take on New Zealand in the final on Sunday after the Black Caps defeated England in the first semi-final – also by five wickets – on Wednesday.