Fognini bested Berlocq 7-6 (7-5), 4-6, 6-1, 6-4 in the first reverse singles match, giving the Italians an insurmountable 3-1 lead in the best-of-five series.
Fognini's heroics put Italy into the Davis Cup quarterfinals for just the second time since 1998. They will go on to face the winner of the United States-Britain match-up in April.
Argentina, meanwhile, was ousted in the opening round for the first time in 12 years.
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