The Istanbul Giants were a goal down after just two minutes when Gaitan capped off a well worked free-kick.
The former Arsenal forward started out on the right wing and scored his first Champions League goal of the season in the 33rd minute when he got on the end of a pass from Chedjou.
Selcuk Inan scored Galatasaray’s first goal in the 19th minute from the penalty spot.
Galatasaray currently have four point from free games after losing against Atletico Madrid in Istanbul and drawing to Astana in Kazakhstan.
GALATASARAY v BENFİCA
Stadium: Türk Telekom Arena
Referee: William Collum
GALATASARAY: Muslera, Sabri, Chedjou, Hakan Balta, Carole, Bilal Kısa, Selçuk İnan, Sneijder, Yasin, Podolski, Umut
MANAGER: Hamza Hamzaoğlu
BENFİCA: Julio Cesar, Luisao, Jardel, Almeida, Nelsinho, Samaris, Gaitan, Pereira, Mitroglou, Goncalves, Guedes
MANAGER: Rui Vitoria