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.
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.
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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)
