Man-of-the-match Faulkner gave away just 27 runs and was helped by another impressive performance by young leg-spinner Adam Zampa, who took two for 32.
Australia, batting first on a green-tinged pitch, lost three wickets in quick succession, with fit-again paceman Wahab Riaz doing the initial damage by bowling in-form Usman Khawaja for 21 and castling David Warner on nine.
Aaron Finch went next, bowled by left-arm spinner Imad Wasim for 15 to leave Australia struggling on 57-3.
Smith, however, steadied the ship aided first by Glenn Maxwell (30 off 24 deliveries) and then by the big-hitting Shane Watson.
Watson struck four fours and three sixes to race to an unbeaten 44 off 21 deliveries as Australia took 66 runs off the last five overs.
Pakistan got off to a poor start, losing Ahmed Shehzad for one, and Faulkner picked up the key wicket of opener Sharjeel Khan who smashed six boundaries en route to a quick-fire 30.
Zampa got into the act by getting Pakistani skipper Shahid Afridi stumped for 14 and bowled Umar Akmal, who was looking dangerous after racking up 32 in 20 balls.
But Faulkner took the plaudits with a match-winning performance, bowling the settled Khalid Latif (46 off 64 balls) before striking again next ball to get Wasim.
He was at it again at the death, dismissing Sarfraz Ahmed and Riaz with his first two deliveries as Pakistan, who needed 30 runs from the last six balls, ran out of steam.
The win took Australia to second place in the five-team group, behind New Zealand, who are already through to the semi-finals and ahead of India in third due to a superior net run rate.
Pakistan are fourth in the table ahead of Bangladesh, with one win and three defeats in four games.
(Reporting by Simon Jennings in Bengaluru, Editing by Ed Osmond)
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