Barty and Dellacqua, who were seeded eighth, lost in three Grand Slam finals this year and are still seeking their first major title.
Hlavackova also won this year's mixed doubles championship at the US Open, hoisting the trophy with Max Mirnyi on Friday.
The Czechs lost in the US Open, Wimbledon and Olympic finals last year. They beat the Williams sisters in straight sets in the semis Friday.
On Saturday, Hlavackova and Hradecka were broken to open the second set, but immediately broke back.
The 17-year-old Barty and 28-year-old Dellacqua also lost in Australian Open and Wimbledon finals.