Benfica are top with nine points from four matches above Atletico Madrid on seven, after they drew 0-0 at Astana, who have two. Galatasaray are third on four points.
Gaitan was dismissed in the 85th minute for a second yellow card after a foul and will miss the next match against Astana.
Jonas opened the scoring for the Portuguese with his first goal in the competition this season after the ball came to him near the penalty spot after 52 minutes.
Six minutes later, the Istanbul side equalised when Lukas Podolski fired past Julio Cesar from inside the box.
Benfica went back in front when long-serving captain Luisao fired into the top corner from inside the area in the 67th.
Galatasaray tried hard to level the scores again and created several chances but failed to find the net.
(Writing by Ece Toksabay; editing by Ken Ferris)
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