The team collapsed in hugs and tears after securing the bronze, having overcome a poor start to the Olympic tournament and a shockingly bad second quarter against number 4, France.
The European champions, ranked 14th in this tournament, felt immense pressure to win a medal for a country where basketball is big, but women's basketball has struggled. There is no big league and most players have to go abroad to play.
"It was so hard for us to do this," said Coach Marina Maljkovic. "Try to understand, this is a poor country, a small country with many difficulties, this is all due to this generation."
It was the Serbian women's first medal game since becoming an independent nation. Yugoslavia's women won silver in 1988, but Maljkovic noted that the country was six times bigger than Serbia.
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"We will drink all night and probably all day tomorrow at the beach and we'll just be happy, but the biggest moment will be when we come to Serbia," said guard Ana Dabovic. "This medal is big."
It came close to not happening at several junctures.
First, Serbia lost its first three games in Rio. Forward Jelena Milovanovic, Saturday's top scorer with 18 points, joked that "we love to start like that, so people underestimate us."
In the bronze medal match, they got a strong start only to fall apart in the second quarter, allowing France to tie the score at 27-27 at halftime.
"Our coach got extremely mad at us, she didn't want to talk to us and then she yelled at us and ran out of the locker room," said Milovanovic.
"I had to do something to provoke them," said Maljkovic.
For the French, the silver medallists in London 2012 who lost in semifinals to the heavily favoured U.S. team, their defeat was a sad ending.
"We had difficulties all through the match to settle our game," said coach Valerie Garnier.
Later in the day, the United States will play for its sixth straight gold medal in the final against Spain, a country that has never medalled in women's basketball.
The Serbian men's team will play for the gold medal in the final against the United States on Sunday.
(Additional reporting by Steve Keating; Editing by Ed Osmond and Nina Chestney)
