The Australians matched the tally of 151 achieved by Pakistan late on Friday, sending the match to the single over shootout, in which they scored 11 runs only for the hosts to edge them by a single run off the last ball of the match.
Having been beaten by seven wickets in their first match against Pakistan earlier in the week, Australia lost the series 2-0 and dropped behind Ireland in the International Cricket Council (ICC) rankings.
Australia skipper George Bailey, who hit a brilliant 42 off 27 balls in the losing effort, was nevertheless upbeat after an improved performance by his team.
"I'm really pleased that we played a lot closer to what we're capable of," he added. "I think our guys will take a lot of confidence out of it. But to be so close, and then to lose, leaves a lot of questions in your head."
Australia, losing finalists at the last Twenty20 World Cup in 2010, have been grouped with Ireland and West Indies in the opening stage of the fourth version of the tournament, which takes place in Sri Lanka from September 18 to October 7.
Pakistan, who won the second Twenty20 World Cup in 2009 and are ranked fourth in the world, will play New Zealand and Bangladesh in their group matches.
