'Dancing With the Stars' Karina Smirnoff -- From Ukraine to the Valley ... What a Country!!

Super hot Ukrainian dancer Karina Smirnoff just turned her "Dancing With the Stars" winnings into a brand new mansion ... in the San Fernando Valley -- which beats living under Soviet rule. Barely.

The season 13 champ -- who was born during Ukraine's U.S.S.R. days -- just dropped $1.35 million on a 6,350-square-foot crib in Woodland Hills, CA.

According to docs, Karina took out a loan for $600,000 -- meaning she laid down some serious up-front cash.

The 5-bedroom, 5-bath pad is rockin' two-story vaulted ceilings, travertine floors, giant hanging chandeliers, huge spa-style tub and steam shower.

Take that, communism!