Turkey got the go-ahead basket in a frantic final minute when Tunceri corralled a loose ball lost by teammate Hedo Turkoglu and drove along the baseline.
After a timeout, Novica Velickovic caught a lob pass but his midair attempt was denied by Erden.
"It was nothing except luck," Turkey coach Bogdan Tanjevic said of the finish. "They played the better game."
Tunceri scored eight points in a crucial 14-3 fourth-quarter run that put Turkey up 78-75 with 3:20 left.
"Unfortunately I think we lost our concentration under pressure the last couple of minutes," Serbia coach Dusan Ivkovic said.
Turkoglu, the Phoenix Suns forward, scored 16 points for Turkey, while Marko Keselj led Serbia with 18.
"It was a very tough loss for us but we have to think about next game, the bronze medal game," Milenko Tepic said.