Azarenka overpowered Kurumi Nara 6-3, 6-3 before being pressed into action again as an emergency doubles replacement after Ayumi Morita had stunned Aliaksandra Sasnovich to take the tie to the wire.
Japan's hopes of completing an unlikely comeback after Morita's gritty 7-6, 4-6, 6-4 win were dashed when Azarenka and Olga Govortsova saw off Morita and Shuko Aoyama 6-3, 6-4 to seal promotion for Belarus.
Azarenka, a two-time Australian Open champion who topped the women's world rankings three years ago, needed an hour and 30 minutes to wrap up her second singles win following a delay to close the roof due to rain.
Azarenka dropped just three games in beating Doi in Saturday's opener, but Nara levelled by wearing down Govortsova in the reverse singles.
As Kei Nishikori continues to blaze a trail for Japan in the men's game, Japan's women have struggled to make a significant impact on the sport since Kimiko Date reached number four in the world in 1995.
They reached the Fed Cup semi-finals in 1996 after Date memorably beat Steffi Graf 12-10 in the third set of an epic match against the German in Tokyo. Belarusian players competed under the Soviet Union flag until 1991.