Life expectancies are heavily biased by infant mortality, in general, but for the period that you're talking about, this is not the major factor. Compare life expectancy at birth and at twenty years (figures 5 and 6 here), and you see the same inflection point around 1970. Infant mortality did decrease a bit more sharply starting then (figure 9), but that doesn't explain the change.

If you look at by-cause mortality, you see a sudden and steep drop in the (age-adjusted) death rate for cardiovascular events (figures 1 and 2 here). (If you don't adjust for age, you see a rise in cancer deaths, but that's because people started living long enough to get cancer, not because they were getting sicker; it's very easy to make that kind of error.)

From that second paper:

The decline in cardiovascular mortality during the last two decades is the best evidence available of the effectiveness of the prevention and treatment initiatives introduced to control these conditions, although it is far from clear what the relative effects of various initiatives have been. Changes in diet (with reduction in animal fat and salt intake), reduction of tobacco smoking, and better control of hypertension, in addition to treatment of established cardiovascular disease, are likely to have contributed to this decline. However, the nearly simultaneous decline in mortality for both sexes argues against a major contribution from reduction in cigarette smoking.

It looks like mortality declined in Australia for the same reasons it did in the United States and the United Kingdom--people stopped dying of heart disease as young as they previously had, though the exact reasons are unclear. But it is interesting to note that heart disease wasn't a significant cause of death before the mid-20th century; the smooth decrease in overall mortality masks a series of changes--people used to die largely from infections, then largely from heart disease, now mostly from (later on) heart disease, cancer or pneumonia. (The death rate from heart disease in the United States today still exceeds that in 1920, but it's age-related.)

At least in the United States, the cause of the fall in cardiovascular mortality is related to a fall in the incidence of atherosclerosis, fewer acute myocardial infarctions (heart attacks), and less damage from the AMIs that do happen. Sufferers are also much more likely to survive: fatality rates for AMI patients under 65 went from 16% to under 2% from 1970-2010, and from 38% to 7% for those 65 or older, for example.

Sources

Richard Taylor, Milton Lewis and John Powles (1998), "The Australian mortality decline: all-cause mortality 1788-1990". Australian and New Zealand Journal of Public Health 22(1).

Richard Taylor, Milton Lewis and John Powles (1998), "The Australian mortality decline: cause-specific mortality 1907-1990". Australian and New Zealand Journal of Public Health 22(1).

James E. Dalen, Joseph S. Alpert, Robert J. Goldberg, and Ronald S. Weinstein (2014), "The Epidemic of the 20th Century: Coronary Heart Disease". The American Journal of Medicine 127(9).