The victory allowed Khimik to bounce back from last week's 88-78 setback at KK Zagreb to improve to 2-1 in Group F.
Popovic, who replaced coach Dmitriy Bazelevskiy, appeared to be in danger of losing in his opening night on the bench after Antonio Graves scored to give Galatasaray a 48-40 lead early in the second half.
Khimik responded by scoring eight straight points to tie the game.
Marton Bader hit a jump shot, Wykeen Kelly made a lay-up, Olu Famutimi dunked and Bader sank another jumper to knot the game at 48-48 with 7:32 to go in the third quarter.
Hüseyin Besok stopped the rot for the Turkish team with a jumper to make it 50-48, only for Oleksandr Kolchenko to connect from long range and Bader to again hit a jumper for a 53-50 Khimik advantage.
Popovic's team stayed in front the rest of the game.
They took a 69-56 lead into the final quarter and blew the game wide open.
A Famutimi jumper put the hosts on top at 78-59 with 6:29 to go.
Murat Özyer's Galatasaray managed to reduce the deficit to 12 by the end of the game but they never threatened to come all the way back.
Kelly and Sasa Bratic wreaked havoc with their three-point shooting for Khimik.
The former was five of eight from the arc and finished with 21 points while Bratic made four of six shots from long range and scored 18.
One very big reason Galatasaray crashed to their second defeat in three games was Khimik's hegemony on the boards.
They finished with 45 rebounds to just 31 for Galatasaray.
Bader and Besok each had 13 for their respective sides.