Led by French guard Fabien Causeur and 19-year old Slovenian Luka Doncic, who was named the season's most valuable player after Friday's 92-83 semi-final win over CSKA Moscow, Real forced Fenerbahce into submission thanks to ironclad defending.
Causeur netted 17 points for Real and Doncic, widely expected to be among the top picks at next month's NBA draft in New York, added 15 with a mature performance which silenced 12,000 fervent Turkish fans in the Belgrade Arena.
Italy forward Nicolo Melli stood out for Fenerbahce with a game-high 28 points but his blistering individual display could not save the Turkish side, who committed a flurry of turnovers and missed plenty of open shots.