Carlo Ancelotti's side shrugged off the first-half dismissal of Sergio Ramos, the 17th red card of his Real career, with goals from Gareth Bale, Alvaro Arbeloa, Angel di Maria and Isco eclipsing Umut Bulut's strike.
Ramos's match was ended for a foul on Bulut after just 26 minutes, although the Turkey international appeared to make the most of minimal contact when he was through on goal.
Bale rifled in a long-range free-kick eight minutes before the interval, only for Bulut to level almost immediately.
However, Arbeloa provided a collector's item of a goal in the second half, finding the net for the first time since November 2010, Di Maria added the third and Isco completed the scoring nine minutes from time to wrap up Group B's top spot for the host.
Real was without Cristiano Ronaldo (thigh), who was nonetheless the centre of attention in the build-up as the Real fans showed their support for the forward's bid to be crowned FIFA Ballon d'Or winner by displaying banners and wearing masks of the Portuguese's face.
Coach Carlo Ancelotti also rested Xabi Alonso, Karim Benzema and Alvaro Morata, with Jese selected up front and Casemiro handed his debut in the competition.
Opposite number Roberto Mancini, who was not in charge when the Turkish side was humbled 6-1 in the reverse fixture, left Burak Yilmaz and Wesley Sneijder on the bench.
Real should have taken the lead inside the opening four minutes when Bale was sent racing clear by Isco, but the Wales star side-footed wide with only the goalkeeper to beat.
The home side threatened again six minutes later as Marcelo cut in from the left and tried to pick out Jese, but Selcuk Inan's desperate challenge denied the Spaniard a shooting opportunity.
Inan also had the visitor's first sight of goal but flashed an ambitious long-range shot over the bar from a tight angle in a rare Galatasaray attack.
But the momentum threatened to shift when Ramos, who was the last man, was given his marching orders after making the slightest of contact with a goal-bound Bulut.
Jese had to make way in the tactical reshuffle as Nacho was introduced, but Bale put the 10 men ahead eight minutes before half-time with a dipping 25-yard free-kick that looked to have deceived Eray Iscan.
The lead was short-lived, however, as Bulut collected Didier Drogba's pass before coolly slotting past Iker Casillas two minutes later.
Real went back ahead six minutes after the restart, Di Maria swinging in a low cross from the left to find the most unlikely of scorers in Arbeloa, who tucked home with surprising confidence amid suspicions of offside.
Arbeloa's spell in the spotlight did not end there and he was booked for diving in the 55th minute, before turning provider for Di Maria with 63 minutes gone.
Casillas produced a stunning save from Drogba's header before Isco added the fourth with a clever turn and finish in the box and there there was no way back for Mancini's side, which must now beat Juventus in the final group game to qualify.