The visitors started well in the first half before the Indian bowlers struck twice. Ravichandran Ashwin got the first wicket while Shami scalped the second.
Australia trounced Pakistan by 7 wickets in the second T20I match on Tuesday to lead the three-match series 1-0 after the first match between the two sides got washed out.
Riding on 80 not out off 51 from Steven Smith, who was declared the Man of the Match, the Aussies chased down the 151-run target with 9 balls to spare.
Earlier on Tuesday, Babar had won the toss and elected to bat at Manuka Oval in Canberra.
However, the decision turned out to be a wrong one as none apart from Babar and Iftikhar Ahmed could dig in their heels.
Babar scored 50 runs off 38 balls before getting run out by David Warner. His innings included six boundaries. Meanwhile, the skipper’s teammate Iftikar scored unbeaten 62 off 34 balls. His quick-fire innings included 5 boundaries and 3 sixes.
Apart from the two Pakistani batsmen, the innings belonged to the Australian bowlers, who took the better of Pakistan as the Men in Green never really got going and lost wickets at regular intervals.
For Australia, Ashton Agar was the pick of the bowlers with the figures of 2 for 23.
Kane Richardson conceded 22 runs in the penultimate over which helped Pakistan reach a competitive total of 150 for 6. Richardson ended with the figures of 1 for 51.
However, the target could not trouble the hosts as Smith smashed 11 boundaries and a six to take Australia home.
Mohammad Irfan with the figures of 1 for 27 was pick of the bowlers for Pakistan but not good enough to win the match for the Green Brigade.