Dmitry Popko did not turn out for the dead rubber against Guido Pella.
Argentina became the third team to be relegated the year after winning the crown, following in the footsteps of France in 1997 and Sweden in 1999.
"Schwartzman did everything he could to switch the momentum, he fought really hard but in the big moments Mikhail played unbelievable tennis. He's the hero of this tie," Kazakh captain Dias Doskarayev told the tournament website (www.daviscup.com).
The Argentines, who won their first title 10 months ago, were without leading players Juan Martin del Potro and Federico Delbonis, who both opted not to play having helped their country to win the 2016 final against Croatia in Zagreb.
They will play in the Group One Americas zone next year.
"We've got to let some time pass and think what each one of us could have done better... those of us who came here and those who didn't," said world number 28 Schwartzman.
"We'll have good chances of getting back into the world group," he was quoted as saying by the Argentine daily La Nacion.
(Reporting by Rex Gowar, editing by Julien Pretot and Clare Fallon)
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