One can add to these the only two test match ties both involving Australia as well!
Here are the recent closest results (by runs) for Australia together with intermediate scores in their final innings. (By recent, I mean after 1929!)
lost by 1 run vs WI, 92/3 (7/74 chasing 184)
lost by 2 runs vs Eng, 2005 (7/137 chasing 282)
lost by 3 runs vs Eng, 82/3 (9/218 chasing 292)
lost by 5 runs vs SA, 93/4 (8/75 chasing 117)
lost by 7 runs vs NZ, 11/2 (9/199 chasing 241)
lost by 12 runs vs Eng, 98/9 (3/130 chasing 175)
lost by 12 runs vs Ind, 04/5 (7/58 chasing 107)
All were losses, but in all but one case Australia was way behind and did well to come as close as it did!
The first recent case of a close win to Australia was in 92/3 versus Sri Lanka (16 runs). That time it was Sri Lanka’s turn to collapse (2/127 chasing 181) after a first innings lead of 291!
On the plus side for Australia, its narrowest wins (after 1977) while chasing have all come against South Africa in South Africa: