The Europeans upset France 90-85 in their semi-final, setting up a clash against hot favourites USA on Sunday.
The clash in Madrid will mark Serbia's first finals appearance since 2002, when Yugoslavia won the trophy.
Serbia's players and coach were full of emotion after their win over France.
"We did an amazing job. We need to rest and then we will play one more game against the USA," Serbian forward Nemanja Bjelica said.
Centre Miroslav Raduljica is looking forward to the clash against the US, who are expected to lift the trophy.
"It's a special game. Finals are always a special game, especially in a big competition like the World Cup," he said.
Milos Teodosic (14 points per game) has been Serbia's best scorer, while Raduljica (13.5) has also been a good contributor.
But they will need to be at their defensive best to deny the US.
James Harden (13.1), Anthony Davis (13), Klay Thompson (12.8) and Kenneth Faried (12.5) are among those to have starred in Spain.
Serbia's Nikola Kalinic hailed his side's defence against France, and said they were happy to be "boring".
"The first two, three quarters we played great defence and got a lot of easy points," he said.
"That's the most important. We are boring - just defence, defence, defence."
All the pressure will be on the USA, who have been expected to win the tournament from the outset.
Only Spain were considered capable of challenging the US, but the hosts were beaten by France in the quarter-finals.
But unless Serbia have recovered physically and emotionally, they are unlikely to stop the US from winning gold for the fifth time.
It would see the Americans equal Yugoslavia as the most successful teams in the tournament's history.