It is named after the 35th Premier of South Australia, Don Dunstan, who represented Norwood for Labor from 1953 to 1979.

Following the 2016 redistribution, the cityside suburbs of Rose Park and Dulwich, previously in Bragg, were added to Dunstan.

Liberal MP Steven Marshall, the last member for Norwood, successfully transferred to Dunstan at the 2014 state election while serving as Leader of the Opposition.

Ahead of the 2022 state election, Dunstan was pushed further east, picking up the Kensington towns while losing Felixstow, Glynde, Rose Park and Dulwich.

As a result, Dunstan is now the most marginal seat in the legislature, with Marshall sitting on a majority of 0.5 percent.