Carlos Berlocq shook off a first-set loss and gave Argentina the first point of the series with a 4-6, 6-0, 6-2, 6-1 decision over Andreas Seppi. Fognini answered with a 7-5, 6-2, 6-2 win over Monaco.
The winners of Saturday doubles match between Italians Simone Bolelli and Filippo Volandri and Argentines Eduardo Schwank and Horacio Zeballos will give their team an edge going into the Sunday reverse singles.
Sunday's schedule calls for Friday's winners -- Berlocq and Fognini -- to meet in the first match, with Monaco and Seppi set for the fifth match of the best-of-five series.
The winner of a series between Great Britain and the United States takes on the Argentina-Italy victor in the Davis Cup quarterfinals in April.
Berlocq took nearly two-thirds of the points after dropping the first set against Seppi. Seppi was 2-of-3 on break chances in the first set but 0-for-4 after that.
Fognini also dropped his serve twice in the first set but answered with three breaks of his own and then two in each of the second and third sets.