Short-handed Real rolls past Gala
Ramos had the hosts in trouble after a red card was brandished just 26 minutes in when he sent Umut Bulut to the ground.
Madrid rallied after the setback, with Gareth Bale scoring with an exquisite free kick from 30 meters in the 37th minute.
Bulut equalized a minute later but the Turkish club wilted in the second half as Alvaro Arbeloa, Angel Di Maria, and Isco all scored to complete an emphatic win at the Santiago Bernabeu Stadium.
Madrid has 13 points and will finish top of Group B regardless of its result at FC Copenhagen in the last matchday.
Galatasaray must beat Juventus, which beat Copenhagen 3-1 on Wednesday, in a winner-takes-all game to advance.
Madrid featured a makeshift starting lineup with Ronaldo and Sami Khedira injured, and Luca Modric suspended.
Jose Rodriguez led the attack in front of Bale, Isco and Angel Di Maria, while Karim Benzema and Xabi Alonso were left on the bench - the latter in place of Asier Illarramendi. Carlos Casimero was given his first Madrid start in midfield.
Bale wasted no time in trying to lay down his claim as the catalyst up front, but he side-footed wide four minutes in with only goalkeeper Eray Iscan left to beat.
There was little excitement until Ramos was sent off for getting a hand to Bulut on the edge of the area, and Selcuk Inan curled the ensuing free kick straight at goalkeeper Iker Casillas.
Bale gave Madrid the lead when he floated a free kick that flew high before dipping over Iscan. Only Ronaldo could probably emulate the Wales international's goal.
But the momentum didn't last, with midfielders Casemiro and Illarramendi failing to set the tempo.
Galatasaray striker Didier Drogba perfectly toe-poked with the outside of his foot to meet the run into the box of Bulut, who slid his shot under the onrushing Casillas to equalize.
Madrid was the better team after the break and Di Maria found Arbeloa in the area with a cross from the left, the Madrid defender dragging his foot back to meet the pass in the 51st minute and guide home his first goal in three years.
Alonso came on as Madrid steadied and, after a near-miss from Arbeloa, the home side scored a deserved third as Di Maria completed a clever buildup in the 63rd.
Modric's absence gave Isco a rare start, and the Spain international dribbled free inside the area before coolly sliding home in the 81st.
Apart from setting up the Galatasaray's opener, Drogba hardly made his presence felt until the 71st when Casillas leaped to tip his driving header over the bar.
Juventus has six points while Galatasaray and Copenhagen both have four.