The Group D clash was sent into overtime after Zoran Erceg sunk a three-pointer to level the score at 82-apiece with only seconds remaining on the clock in Istanbul.
Galatasaray and Zvezda exchanged leads in the first additional period, with the home team opening a four-point buffer early on.
Zvezda wrestled back the lead, thanks in part to Marcus Williams and his 17th assist of the game - a Euroleague record, but the see-sawing battle continued with a second overtime needed after Carlos Arroyo tied the match at 96-96 from the free-throw line with 11 seconds left.
Erceg and Arroyo starred, the pair helping the Turks to a five-point lead with 2:30 to play.
The Serbian visitors refused to go away but Arroyo put the game out of reach with two three-pointers in quick succession taking his tally to six for the evening.
Erceg finished with a game-high 32 points and seven rebounds, while team-mate Arroyo had 26 points and six assists as Galatasaray moved to a 3-3 win-loss record alongside Zvezda.
Luka Mitrovic (30 points) led the way for Zvezda, while Boban Marjanovic (23 points, 17 rebounds) and Nikola Kalinic (21 points) made contributions in the road loss.
Real Madrid escaped Lithuania with a narrow 68-66 win over Zalgiris.
The Group A leaders, who boast a 5-1 record, were helped by a 12-1 run in the final quarter as they edged their Lithuanian hosts at Zalgirio Arena.
Sergio Rodriguez (14 points, nine assists), Sergio Llull (11 points) and Andres Nocioni (11 points) were the stars for Real.
Zalgiris (3-3) were led by James Anderson (21 points) and Paulius Jankunas (17 points).
The only other clash in Group A saw Nizhny Novgorod account for Dinamo Banco di Sardegna Sassari 89-82.
Meanwhile, Unicaja were 82-73 winners over Cedevita Zagreb in Group B.