Madrid had to play just under three quarters of the game with a man less after Sergio Ramos was shown a red card for dragging back Umut Bulut as he broke clear on goal.
Bale then opened the scoring with his fifth goal in six games, but Bulut equalised for the Turkish champions just a minute later.
Alvaro Arbeloa restored Real's lead just after the break and the full-back then teed up Angel di Maria to make the points safe 12 minutes later.
And Isco rounded off the scoring with a wonderful piece of skill as he left Selcuk Inan on the floor before side-footing the ball home.
Victory seals Madrid's place in the last 16 as group winners, whilst Galatasaray will have to beat Juventus at home on matchday six if they are to qualify after the Italian champions beat FC Copenhagen 3-1 in the night's other match in Group B.
In the absence of the injured Cristiano Ronaldo, Bale was expected to carry more of the responsibility in attack, but he passed up a huge chance inside three minutes when he slotted wide with just Eray Iscan to beat.
The hosts were then reduced to 10 men after just 26 minutes when Ramos pulled back Bulut as he raced onto a ball over the top and Scottish referee Willie Collum had no hesitation of brandishing the 17th red card of Ramos' Madrid career.
Madrid coped admirably despite the sending-off and were in front on 37 minutes when Bale sending a dipping free-kick from fully 35 yards into the top corner.
The lead lasted barely 60 seconds, though, as a wonderful through ball from Didier Drogba played in Bulut to level. Bale should have restored Madrid's lead when he fired an effort just over from inside the area.
But Los Blancos did make it 2-1 just six minutes after the interval through an unlikely source as Arbeloa bundled home Di Maria's cross.
Arbeloa then saw another effort fly just wide before venturing forward once more to square for Di Maria to make it 3-1.
Galatasaray boss Roberto Mancini introduced former Real favourite Wesley Sneijder in a bid to turn the game around.
And Iker Casillas had to make a stunning save to prevent Drogba's looping header from setting up a grandstand finish.
But Isco rounded off a fine night for the hosts when he danced through the Galatasaray defence before slotting low into the net.