The hosts, who had not won in their last 10 European fixtures, responded magnificently to their early setback to beat a Benfica side who had won their two opening Champions League group fixtures.
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Benfica winger Nicolas Gaitan continued his excellent Champions League goalscoring form when he notched his third in as many games with a delicate finish inside the opening two minutes.
The goal woke Galatasaray up, however, and Wesley Sneijder led the fightback as he tested Julio Cesar with a long-range free kick, then planted a corner straight onto the head of Hakan Balta only for the defender's effort to be flicked clear by Cesar.
Galatasaray's first-half comeback was then completed when Lukas Podolski drilled an effort under the body of Cesar just after the half-hour mark.
Sneijder saw his deflected strike cannon off the upright just minutes after the restart, before Umut Bulut's point-blank header from the Dutchman's corner was acrobatically saved by Cesar with his legs.
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Podolski then collected Sneijder's pass and riffled a powerful shot inches wide of Cesar's upright as the home side tried to put the game to bed.
One of the night's biggest cheers came as Burak Yilmaz completed his comeback from injury with a 15-minute cameo appearance from the bench.
The striker couldn't score the goal that would have made the final minutes a more comfortable experience for Hamza Hamzaoglu, but despite a late push by Benfica, Galatasaray held on for all three points.