Real dominated the early stages on a chilly and blustery night at the Bernabeu but were rocked back when defender Ramos was shown a straight red card in the 26th minute for impeding forward Umut Bulut when he was through on goal. (Agencies)
The Turkish champions were unable to make their numerical advantage count and Gareth Bale put Real, who were missing injured top scorer Cristiano Ronaldo, ahead with a superb free kick 11 minutes later.
Galatasaray levelled within a minute when Didier Drogba sent Bulut clear and he slid the ball past Iker Casillas before fullback Alvaro Arbeloa restored Real's lead when he netted his second Champions League goal six minutes after halftime.
Angel Di Maria struck in the 63rd minute and Isco scored from close range nine minutes from time to seal a comfortable victory for the nine-times European champions, who are chasing the 10th continental crown that has eluded them since their last triumph in 2002.
"I think we started a bit slowly in the first half but later with 10 men the team played very well," Real coach Carlo Ancelotti said in an interview with Spanish television broadcaster Canal Plus.
"We controlled the match efficiently and pressured high up the pitch," added the Italian, who was clearly upset with Ramos after he was sent off for the 17th time in his Real career.
With his side virtually assured of a place in the knockout round, Ancelotti included a number of youngsters in his starting lineup with regulars Xabi Alonso and Karim Benzema on the bench.
Casemiro and Asier Illarramendi were deployed in the holding midfield positions and Isco played in a central creative role behind forwards Bale, Di Maria and Jese.
Record signing Bale should have put Real ahead in the fourth minute but the Wales winger placed his low shot narrowly wide with only keeper Eray Iscan to beat.
After the dismissal of Ramos, Ancelotti immediately withdrew Jese and brought on Nacho at centre back, and it was the home side who struck first when Bale's swerving long-range free kick deceived Iscan and flew over his head into the net.
Bale's goal marked the 30th consecutive match Real have scored in the Champions League, beating the record set by arch rivals Barcelona between November 2009 and March 2012.
Didier Drogba's brilliant pass with the outside of his foot to set up Bulut for the equaliser was one of the highlights of the match, but the visitors were unable to inflict further punishment on a Real side bristling with quality.
Arbeloa was allowed space to clip home a Marcelo cross before the former Liverpool fullback set up Di Maria to fire in a low shot from the edge of the area.
Isco followed up his own shot and showed wonderful composure to beat his marker and score Real's fourth.
"The team was very, very good in the second half," Arbeloa, whose goal and assist earned him a rousing ovation from the Real faithful, told Canal Plus.
"The coach was exactly right in the tactical changes he made," added the former Liverpool man.
Defeat for Galatasaray leaves Roberto Mancini's side in third in the group with one game to play.
Real are top on 13 points, Juventus are second on six after their 3-1 win at home to FC Copenhagen on Wednesday, and Galatasaray and the Danish side each have four points.
In the final round of matches in the group on Dec. 10, Real play at Copenhagen and Galatasaray host Juventus.
"We played some excellent football in the first half but I do not know what happened in the second half," Mancini said.
"If you make mistakes, then a team like Real Madrid will make you pay," added the Italian, who turned 49 on Wednesday.
Real dominated the early stages on a chilly and blustery night at the Bernabeu but were rocked back when defender Ramos was shown a straight red card in the 26th minute for impeding forward Umut Bulut when he was through on goal.