After a tight first period, Serbia streaked into a 16-point lead thanks to a 14-0 run midway through the second period as the Russian offence stalled completely.
The Serbs held on to lead by 14 at the break on the back of a towering display by centre Boban Marjanovic, who racked up 13 first-half points and three assists, including a sublime bounce pass to Vladimir Lucic for an easy basket.
The resilient Russians, who beat Serbia 75-72 during the group stage, mounted a superb fight back with an 11-0 run of their own midway through the third period, eventually closing the gap to just two points early in the fourth quarter.
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Guard Alexey Shved notched 33 points and five assists on the night, but Russia could not rein in the Serbs, who had a wider array of offensive weapons at their disposal.
Bogdan Bogdanovic called on all his experience to hit a three for Serbia with 1:44 left to make it a seven-point lead, and followed it up with a two-point effort 37 seconds later.
A late three-pointer from Shved kept the game alive into the final minute, but Serbia held on to book their berth in Sunday's final.
(Reporting by Philip O'Connor; Editing by Toby Davis)
