Max Purcell and Jordan Thompson clinched the winning point for Australia with a 6-7(3) 7-5 6-4 win over Mate Pavic and Nikola Mektic in a clash that was nearly a rematch of the Wimbledon doubles final until a late player switch.
Moments before the match Australia captain Lleyton Hewitt put Thompson in for Matthew Ebden, who along with Purcell captured the Wimbledon doubles title when they beat defending champions Pavic and Mektic in the All England Club final.
The first set was a tightly-contested affair until the Croatian duo stepped it up and rolled through the tiebreaker but Purcell and Thompson never wavered and broke for a 6-5 lead in the second frame and held serve to force a decisive third set.
Purcell and Thompson broke again for a 4-3 lead and that was all the cushion they needed as they took care of business on their next two service games to put Australia into their first final since 2003 - when they won their 28th title.
Australia's Alex de Minaur forced the decider when he overpowered Marin Cilic 6-2 6-2 after Borna Coric gave Croatia an early lead with a 6-4 6-3 win over Thanasi Kokkinakis.
De Minaur did not face a single break point during a match that lasted only 44 minutes while Cilic struggled mightily from the service line with 10 double faults.
Coric had put Croatia on course for a second successive appearance in the Davis Cup final with a commanding display against Thanasi Kokkinakis in which he blasted 18 winners against just nine unforced errors.
Canada play Italy on Saturday with the final scheduled to be played on Sunday.
