Gareth Bale, Alvaro Arbeloa, Angel Di Maria and Isco were all on target as Carlo Ancelotti's men dented their Turkish opponents' hopes of making the last 16
The Spain defender received his marching orders with the scores locked at 0-0 for tugging back Umut Bulut, but Carlo Ancelotti's side soon raced into the lead thanks to a Gareth Bale free kick.
Bulut soon leveled the scores, but Alvaro Arbeloa put the hosts back ahead just after the break, before goals from Angel Di Maria and Isco sealed a resounding victory that clinched top spot in Champions league Group B.
Madrid were without the injured Cristiano Ronaldo, who was nonetheless the centre of attention in the build-up as the fans showed their support for the forward's bid for this year's Ballon d'Or by wearing face masks of the Portuguese superstar.
Coach Carlo Ancelotti arested Xabi Alonso, Karim Benzema and Alvaro Morata, with Jese Rodriguez selected up front and Casemiro handed his debut in the competition.
Opposite number Roberto Mancini, who was not in charge when the Turkish side were humbled 6-1 in the reverse fixture, left Burak Yilmaz and Wesley Sneijder on the bench.
Madrid should have taken the lead inside the opening four minutes when Bale was sent racing clear by Isco, but the Welshman 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 Rodriguez, but Selcuk Inan's desperate challenge denied the Spaniard a shooting opportunity.
Inan also had the visitors' 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 deceived Eray Iscan.
The lead was short-lived, however, as Umut 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 men, who must now beat Juventus in the final group game to reach the knockout stages.