Having lost to West Indies on Saturday, Australia is eliminated, while Sri Lanka has booked its place in the Super 8 phase of the competition.
After losing the toss Australia made a moderate total of 159-9.
Mitchell Johnson and David Hussey were the top scorers, with 28 not out and 28, respectively, as Ajantha Mendis took 3-20 and Lasith Malinga 3-36.
Tillakaratne Dilshan struck a brilliant 53 before he was bowled by Michael Clarke and Kumar Sangakkara then took over, making an unbeaten 55.
Late wickets from Brett Lee gave Australia hope, but just as the momentum appeared to be shifting he conceded a crucial six to Jehan Mubarak that just eluded the fielder on the boundary.
Needing just one run to win off the last over, Sri Lanka reached its target when Johnson bowled a wide.
