The Istanbul club used a 25-15 run in the first quarter, hitting 5/6 from the three point line at Lanxess Arena in Cologne, Germany.
Despite the Russian side's brave effort in the fourth quarter, scoring 31 points, the Turkish club managed to hold on for the final ticket.
Serbian guard Vasilije Micic led Anadolu Efes, scoring 25 points and six assists, as Sertac Sanli finished with 19 points, eight rebounds, and three blocks.
Efes' French guard Rodrigue Beaubois also added 15 points.
In a post-match interview, Anadolu Efes head coach Ergin Ataman said that the team played perfect basketball for three quarters but then they made incredible mistakes in the last quarter.
"All respect to Clyburn. We didn't really stop him. We gave up all the isolation points to Clyburn. We didn't stop him. On offense, we made incredible mistakes. We were lucky to win the game at the end. We deserved to win more easily but we will be in the final... All respect to Clyburn because he broke our defense," Ataman said.
"We had perfect defense for three quarters. Nobody could find scores inside -- Shengelia, Voigtmann. But Clyburn and Hackett [beat us] on the easy pick-and-roll attack. Okay, defensively we made those mistakes, but offensively, especially after Micic had the fifth foul, we stopped playing. But we will play in the final and I hope we will not make these mistakes again in the final," he added.
Efes will play against the winner of the Barcelona and AX Armani Exchange Milan game in the final.