Australia scored only 23 seconds into the final when Bienne Terita stepped Tenika Willison and sprinted 80 meters.
Then Miller scored twice in two minutes, the second from a brilliant offload by Michaela Blyde.
But Australia went into halftime 14-12 ahead after Teagan Levi scored and converted a long-range try she started by forcing a ruck turnover.
Teagan Levi scored again straight after the break after a Terita break but Miller’s hat-trick try tied the score going into the last two minutes.
Earlier, New Zealand booked a place in the women’s final after a 21-19 semifinal victory over Canada with Miller saving the Black Ferns Sevens with a try in the 13th minute.
The All Blacks Sevens finished third after their title hopes ended with a 21-19 semifinal defeat to Argentina. New Zealand were leading 19-7 before Argentina stormed home with two late tries. South Africa won a fifth straight Dubai title when it beat Argentina 12-7 in the final under acting coach Philip Snyman while the All Blacks Sevens finished with a win over Fiji in the third place playoff.
South Africa’s fifth Dubai title in a row tied the series record for most consecutive titles at one site equaling Fiji’s five in Hong Kong from 2015-19.
The next event is in Cape Town next weekend.