Borna Coric, 26th player in the world, first gave Croatia the lead by beating Thanasi Kokkinakis (95th) in the opener, 6-4, 6-3.
The Australians equalized thanks to an in-form Alex de Minaur.
The 24th player in the world, aged 23, left no chance for veteran Marin Cilic (34, 17th), beaten in two sets 6-2, 6-2.
After these two one-sided matches, the doubles was much more balanced.
First set for the Croats in the decisive game (7/3), then 7-5 and finally 6-4 for the Australians Max Purcell and Jordan Thompson, who broke at 3-3 in the decisive set.
The second semi-final will take place on Saturday between Italy, which fell from the United States in the quarter-finals, and Canada, with its two stars Félix Augier-Aliassime (6th player in the world) and Denis Shapovalov (18th).
Davis Cup 2022, first semi-final:
Australia beat Croatia 2-1
Borna Coric (CRO) defeats Thanasi Kokkinakis (AUS) 6-4, 6-3
Alex de Minaur (AUS) beats Marin Cilic (CRO) 6-2, 6-2
Jordan Thompson/Max Purcell (AUS) beat Nikola Mektic/Mate Pavic (CRO) 6-7 (3/7), 7-5, 6-4
© 2022 AFP