Crouch put the Reds in the lead after only eight minutes when he connected with a perfect Fabio Aurelio cross and steered the ball home past Mondragon in the Galatasary goal.
It was 2-0 six minutes later when the Turks failed to clear their defences properly and Jermaine Pennant collected the ball and put a superb cross onto the back post for Luis Garcia to head home his first of the season and his eighth Champions League goal of his Liverpool career.
Despite going 2-0 up the Reds were never completely comfortabe with Topal putting one excellent cross after another into the Liverpool area.
Liverpool must have thought they'd wrapped the game up five minutes into the second half when Peter Crouch scored his second of the night and what was probably the best goal of his Liverpool career.
Just as the game seemed to be over Galatasary breathed life into it however. Subsitute Umit Karan buried two quick headers past Pepe Reina and suddenly it was game on again.
It was a nervy 25 or so minutes for the Reds but they held on for the win to top the group.
