Icardi, who joined the French champions on a season-long loan from Inter Milan at the start of last month, struck from close range early in the second half.
The Argentinian's solitary effort was enough to secure PSG a second straight Champions League win and lift them five points clear of group rivals Real Madrid, who were held at home by Club Brugge.
Turkish champions Galatasaray, seventh in their domestic league after winning only two of their first six matches, drew 0-0 in Brugge in their opening group game and sit above Madrid on goal difference.
Uruguay goalkeeper Muslera denied Di Maria again with a fine save in the top corner and Pablo Sarabia fired his effort just off target as PSG set the early pace.
Ivorian midfielder Jean Michael Seri, on loan from Fulham, pulled Galatasaray's only first-half attempt wide from outside the box and it was one-way traffic as Sarabia's low shot forced Muslera into another fine save.
Galatasaray made a better start to the second half and Seri's long-range shot from a tight angle was saved by Keylor Navas.
But after Di Maria had been denied in a one-on-one with Muslera, PSG took a 52nd-minute lead.
Sarabia provided the assist and Icardi was in the right place at the right time to turn the ball home.
The Turks pressed for an equaliser as the second period unfolded with Falcao firing over from outside the area, but PSG reasserted their authority in the final quarter.
Galatasaray poured forward in stoppage time and Mariano's effort was a fraction too high as PSG held on for victory.