The game started slowly as both sides could not score for almost the first two minutes at the Stark Arena in Belgrade.
Real Madrid finished a slow-paced first quarter, 15-14, in front with their effective offensive rebounds.
Despite Shane Larkin and Vasilije Micic trying to rally Efes by dropping 23 points in the first half, Los Merengues widened their lead to five points at the end of the second quarter, and the first half ended 34-25.
Efes' James Anderson and Real Madrid's Vincent Poirier had a row after a challenge and both players were penalized with an unsportsmanlike foul in the third quarter, which ended with a 42-40 Los Merengues lead.
Anadolu Efes brought the lead at the beginning of the last quarter and managed to stay on top in the end, with German center Tibor Pleiss' vital points, and won the final 58-57.
Micic, who was also selected as the Final Four MVP, dropped 23 points, while Pleiss and Larkin added 19 and 10 points, respectively. Walter Tavares was the best player of the game for Real Madrid with 14 points and 11 rebounds.
The game marked the third EuroLeague win for Turkiye, as Fenerbahce Beko won the 2016-17 title.