They were shocked in the second minute when Nicolas Gaitan put the visitors ahead after he received the ball in the penalty area, stepped inside Aurelien Chedjou and fired past keeper Fernando Muslera.
But Galatasaray captain Selcuk Inan hit back in the 19th minute, scoring from the penalty spot after Andre Almeida handled in the area.
Lukas Podolski put the momentum firmly with the home side in the 33rd minute when he ran on to a long ball from Chedjou along the right and drove a left-foot shot past keeper Julio Cesar.
The second half started with a flurry of goal efforts with both keepers making saves, Wesley Sneijder firing from long distance against the post and Benfica failing to hit the target after some attacking moves.
But the home side gradually fell back into firm defence and kept the Lisbon visitors at bay.
The result still leaves Galatasaray third on four points behind Benfica on six, level on points with leaders Atletico Madrid who beat Astana 4-0.
(Writing by Daren Butler; editing by Clare Lovell)
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