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Bellucci's triumph means the outcome will be decided by the final singles match to come later between American Sam Querrey and Brazil's Thiago Alves.
Serbia awaits the US-Brazil winner in April's quarter-finals.
It took six break-point chances, but 36th-ranked Bellucci finally cracked Isner when the American netted a slice backhand in the eighth game of the final set and then the Brazilian held at love, his 21st held service game in a row, to win.
Isner, ranked 16th, suffered his fifth loss in a row in five-set matches and left the United States in a live fifth rubber for the first time in 13 years trying to avoid squandering a 2-0 tie lead for the first time since 1994.
Querrey and Isner won singles matches on Friday to put the Americans on the brink of advancing but Marcelo Melo and Bruno Soares upset the World No. 1 doubles duo of Bob and Mike Bryan on Saturday to keep the Brazilians alive.
The US squad has won a record 32 Davis Cup titles but taken the trophy only once in the past 17 years.