Argentina forward Icardi joined PSG on a season-long loan from Inter last month, and tapped home from close range in the second half after a slick passing move.
In the face of a hostile atmosphere in Istanbul, PSG showed its mettle and would have won by a greater margin but for Angel Di Maria's poor finishing.
PSG's victory moves it four points clear at the top of the group, with Real Madrid five points adrift after being held to a home draw by Club Brugge.
The catcalls and boos from the Galatasaray fans at the Ali Sami Yen Stadium did not knock PSG off their stride early as they swarmed forward in the early stages.
Di Maria had two glorious opportunities to give PSG the lead but a combination of disappointing finishing and fine goalkeeping kept the scoreline goalless.
Argentina international Di Maria first shot straight at Fernando Muslera when clean through, and then saw the Galatasaray goalkeeper produce a brilliant reaction save to push a shot over the bar.
PSG goalkeeper Keylor Navas kept out a curling free-kick from Jean Michael Seri early in the second half before Di Maria squandered yet another chance when he broke clear only to fluff his lines as Muslera advanced off his line.
Thomas Tuchel's men took the lead seven minutes after the break as some neat build-up culminated in Pablo Sarabia's low cross for Icardi, who calmly stroked the ball into the net.
Icardi was replaced by fit-again Kylian Mbappe on the hour mark and the France striker tested the reflexes of Muslera with a low angled shot that he blocked at his near post.
Galatasaray sporadically threatened as they sought an equaliser but PSG stood firm with little difficulty.