World number two Daniil Medvedev beat Marin Cilic 7-6 (9-7) 6-2 after Andrey Rublev put them ahead in Madrid.
Medvedev was unbeaten throughout the tournament in a year where he won his maiden Grand Slam title at the US Open.
His team become the fourth nation to win both the Davis Cup and Billie Jean King Cup - the women's equivalent team competition - in the same year.
More to follow.
