Jose Mourinho's Blues welcomed star striker Didier Drogba back to west London but the Ivorian had a mediocre night for the Turkish side as the Premier League leaders controlled proceedings in the Round of 16 second leg to move to the final eight with a 3-1 aggregate victory.
Last month's initial bout saw Roberto Mancini's Cimbom step up in the second half to equalise through Aurelien Chedjou after Fernando Torres' early opener but there was none of the same tonight as the Istanbul giants were powerless in the English capital.
Samuel Eto'o, who started in place of Torres, gave Chelsea the lead within five minutes when he latched onto a lovely through ball from Oscar to rifle home past Galatasaray keeper Fernando Muslera from a tight angle.
The visitors were struggling to test the Blues defence while the home side went about doubling their advantage on the night and their attacking prowess paid off late in the first half.
Chelsea skipper John Terry saw his header from a corner palmed away by Muslera but the ball fell straight into the path of an unmarked Gary Cahill who slammed home into the roof of the net from close range.
That set up the 2012 European champions for a second half of keeping the Turkish outfit quiet and it proved to be a simple task as Galatasaray's failure to land one single shot on target denied them any hope in what was a fairly quiet night for Blues keeper Petr Cech.
The victory keeps alive Mourinho's hopes of becoming the first manager to win the Champions League with three different clubs but the games don't get any easier as Chelsea now find themselves alongside the likes of Barcelona, Real Madrid, Paris Saint-Germain, Bayern Munich and Atletico Madrid in the final eight.
2013/14 UEFA Champions League - Round of 16 second leg
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball