Hüseyin Besok had 17 points and nine rebounds for the Turkish team.
Murat Özyer, the Galatasaray coach, said: "It was a very important game for us to qualify from the group and our players have shown they could win although we were missing a couple of players."
Galatasaray fell behind 25-13 eight minutes into the first quarter but stormed back to take a 45-35 advantage at half-time.
KK Zagreb refused to go away, however, and twice pulled level in the fourth quarter at 60-60 and then 62-62.
But Gala kept their composure and went back in front.
A Besok lay-up extended the advantage to 75-68 with 1:49 to go.
They only led by three with six seconds remaining, however, when Cüneyt Erden went to the line for Gala.
He missed the first but made the second four a four-point advantage and that's how it finished.
Zagreb are now 1-3.
Krunoslav Simon of Zagreb said: "We lost a game because we played without motivation both in defense and offense. "We lost to a better team. Because of the defeat, we probably lost any chance of playing in the next rounds of this competition."
Denis Bajramovic, who replaced Zeljko Pavlicevic as Zagreb coach recently, admitted his team had a night to forget:"I take a big part of the responsibility for losing this game and this has been our worst game since I started coaching this team."