Sergio Ramos was dismissed after 26 minutes but Bale gave Madrid the lead 10 minutes later with a curled dead ball effort from 35 yards out. Umut Bulut responded with an equaliser immediately but Roberto Mancini's side crumbled after the break despite having the extra man.
Alvaro Arbeloa, Angel di Maria and Isco all got on the scoresheet to condemn the Italian coach to the heaviest defeat of his relatively short spell in charge of the Turkish champions.
Galatasaray must now beat Juventus at home in a fortnight's time if they are to reach the latter rounds and Mancini is to avoid his fourth exit at the group stage of Europe's elite competition.
Bale was given a dream opportunity to open the scoring with just four minutes on the clock, latching onto a through ball by Isco and beating the offside trap to run through on goal, but he pulled his shot a couple of feet wide of the far post.
Galatasaray's first chance came after 18 minutes, captain Selcuk Inan blazing over the bar after good build up play by his side on the edge of the area.
Ramos was given his marching orders for bringing down Bulut, and although the forward went down easily, Scottish referee William Collum decided that a goalscoring opportunity was being impeded, and showed Ramos a red card.
Real boss Carlo Ancelotti reacted by taking off Jese and replacing him with Nacho to maintain a four-man defence.
The visitors were not emboldened by the red card and less than 10 minutes later it was Madrid who took the lead, Bale striking the dead ball with perfection, sending it curling over the wall and dipping down into the net past inexperienced goalkeeper Eray Iscan.
Mancini's men responded immediately. Didier Drogba curled a pass with the outside of his boot towards Bulut, Pepe was caught out of position and the forward knocked the ball under Iker Casillas to equalise.
Bale could have have put Madrid in front again a couple of minutes before the break, but shot just over the bar as he entered the area
Madrid restored their lead soon enough, albeit from an unlikely source. Di Maria's through ball found its way to the feet of Arbeloa, and the right-back scuffed his shot but still put it beyond Iscan.
It was not the defender's last foray into the opposing penalty area. He was later booked for diving and then volleyed just wide from the edge of the area, before providing the assist for Di Maria's goal. Arbeloa picked up the ball from Isco on the right hand side of the box before squaring to the Argentinian, who took one touch before burying his shot in the net.
The visitors never got going after the break. Bulut had the ball in the net two minutes into the second half but was correctly ruled offside, then he narrowly failed to get any contact on a cross from Eboue.
The closest the Turkish side came to scoring was with a Drogba header that was headed towards goal until Casillas plucked it out of the air to send over the bar.
With 10 minutes remaining Isco added scored his second goal in four days to round off the victory. The 21-year-old beat a man on the edge of the area to create a shooting opportunity, won the ball back after his effort had been blocked then turned another defender in the box before slotting into the net.
The former Malaga man had scored the opening goal when Madrid thrashed Galatasaray 6-1 in their opening group game back in September and had the last word on another night the Turkish side would rather forget.