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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 in the eighth game of the final set, but 36th-ranked Bellucci finally cracked Isner when the American netted a slice backhand. Bellucci then held at love, his 21st held service game in a row.
"I think he was a little bit tired in the end of the last set," Bellucci said. "I was just trying to fight because he was making mistakes.
"For me it's very special. Isner is a great player. Of course he was favored. It's always special to beat him. I'm very happy. He has a big serve. It's not easy to play against him on this type of service."
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. The Brazilians are in the World Group for the first time in a decade.
Bellucci forced a fifth set with a break in the last game of the fourth, Isner denying the Brazilian with two service winners before netting a forehand to drop the fourth set.
In the third, Bellucci fired a 121-mph ace to deny Isner's first break chance in two sets and then held to reach a tie-break.
Bellucci fired a forehand winner for a 6-5 lead but netted a backhand off an Isner half-volley to miss his chance.
Isner botched his second set point by netting a forehand before taking the set on a service winner.
Isner broke Bellucci's first service game of the match and rolled through the opening set only to have Bellucci take the second, equalizing on his third ace of the match.