The result left Galatasaray fourth in its top 16 group, with seven wins and as many defeats, ahead of Lokomotiv Krasnodar on a superior point difference after the Russians beat Bayern Munich 84-75 on Thursday.
Fenerbahçe Ülker also beat Anadolu Efes 84-65 in an all-Turkish encounter between two already eliminated İstanbul teams.
Galatasaray took the last remaining quarterfinal berth to join CSKA Moscow, Real Madrid and Maccabi Tel Aviv, which earlier qualified from Group F, after Barcelona, Emporio Armani Milan, title holders Olympiacos Piraeus and Panathinaikos also advanced from Group E.
In the other crunch game, Real lost the top spot in its group to CSKA after a shock 87-80 defeat to bottom team Zalgiris Kaunas, meaning that it faces a quarterfinal playoff against Olympiacos.
The mouthwatering best-of-five series will be a repeat of last year's final in London's O2 Arena, when the Greek side stunned Real to win its second successive and third overall title.
Milan locks horns with Maccabi and CSKA meets Panathinaikos in the other three playoff ties, with the winners advancing to the May 16-18 final four in Milan.
Needing a win to go through, Galatasaray was cheered on by a sellout crowd in İstanbul but made a jittery start as Partizan took a 13-7 lead midway through the opening quarter thanks to a pair of three-pointers and some fast breaks.
The home side responded with inspired performances from Georgia guard Manuchar Markoishvili and Serbia forward Zoran Erceg, who sank 16 and 13 points, respectively, as former NBA playmaker Carlos Arroyo dished out seven assists to help turn the tide.
Real needed to beat Zalgiris by any margin to overhaul CSKA on points difference but an electrifying display by the written-off Lithuanians produced one of the biggest upsets in the second group stage as American guard Justin Dentmon poured in 36 points for the home side.
On Thursday, Olympiacos claimed bragging rights in a thrilling Athens derby against Panathinaikos after playmaker Vassilis Spanoulis buried an audacious three-pointer on the buzzer to give the holder a 68-65 home win over its bitter cross-town foe.
“It was like a must-win game for us after three successive defeats to Panathinaikos, and Spanoulis won it in the last second thanks to his personality,” Olympiacos coach Georgios Bartzokas told www.euroleague.net.
Guard Kostas Sloukas added: “We are on the bright side of the moon, in good shape and with the proper psychology. Now we are going to the playoffs where we must show passion, energy and intensity."