The Germany international scored in the 33rd minute with the outside of his foot.
The Istanbul Giants were a goal down after just two minutes when Gaitan capped off a well worked free-kick.
Selcuk Inan scored Galatasaray’s first goal in the 19th minute from the penalty spot.
The victory re-ignites the Lion’s Champions League campaign following a disappointing start after losing against Atletico Madrid in Istanbul and drawing to Astana in Kazakhstan.
The Lion’s take on Benfica once again in the next round of UEFA Champions League games.
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