Jamie Baker gave Great Britain the consolation of a lone victory on Sunday as Argentina completed a 4-1 victory in the Davis Cup in Buenos Aires.
Baker recovered after a defeat by David Nalbandian on Friday
Argentina secured the World Group tie in the doubles on Saturday, and extended their lead when Jose Acasuso beat Alex Bogdanovic 7-5 7-5 on Sunday.
But world number 235 Jamie Baker then upset the odds with a 7-6 (7-4) 6-4 win over Agustin Calleri, ranked 41st.
Britain's defeat leaves them facing a World Group play-off in September.
They will hope to have the absent Andy Murray back for that tie, in which another loss would see them relegated from the elite 16-team World Group.
"We came down here for an unbelievably tough ask," Glaswegian Baker told BBC Sport. "I'd like to say a massive thank you to our captain, John (Lloyd).
"During the whole circumstances surrounding Andy Murray not coming, John hasn't faltered, he's been so positive, and I wouldn't rather have anyone else with me out on the court."
The powerful Argentina squad will host Sweden in a quarter-final tie in April.