Olympiakos will meet last season's runners-up CSKA Moscow for a place in the final while eight-times winners Real Madrid will play rivals Barcelona in the other semi-final at London's O2 Arena, which is hosting the showpiece event from May 10-12.
Efes seemed on course for an upset after taking a 40-27 lead in the closing stages of the first half but Olympiakos, roared on by their passionate fans, took control of the tie after levelling at 49-49 midway through the third quarter.
Playmaker Vassilis Spanoulis led the Greeks with a game-high 19 points and forward Giorgios Printezis, who scored last year's title-winner on the buzzer in a 62-61 win over CSKA, chipped in with 15 including a three-pointer in the final period.
Jamon-Alfred Lucas led Efes with 14 points, Serbia forward Dusko Savanovic netted 12 and former Los Angeles Lakers guard Jordan Farmar scored 11 having been tightly marked in the fourth quarter.
- Sports & Recreation
- Real Madrid