The Blues continued to dominate after the break as Didier Drogba struggled to make an impact on his return to the club, and Jose Mourinho's outfit will now await the last-eight draw on Friday morning.
Below, Sports Mole assesses whether Chelsea were deserving of their progress through to the last eight.
On target: 9
On target: 0
Was the result fair?
This was as comfortable a 2-0 result as you will see all season. Chelsea did what they had to do against a limited Galatasaray side, who, for some of the quality in their lineup, did nothing throughout the 90 minutes. Samuel Eto'o's early goal got the Blues off to the perfect start, and his side had their opponents on the run during a dominant showing. However, they are sure to face a much sterner examination in the last eight.
Jose Mourinho would have been aghast at his side's performance at Villa Park on Saturday, but they responded in the best possible way. They were never forced out of second gear, which enabled them to coast through to the final whistle. Oscar and Frank Lampard were the stand-out performers but each player did what was required during a comfortable night.
There is nothing positive that can be said about how Galatasaray played tonight. They somehow had more possession than Chelsea, but they never looked likely to cause a surprise in West London. Didier Drogba looked like a man who had seen his powers disappear, while Wesley Sneijder looked a far cry from someone who was considered one of the best players in Europe not so long ago.
Sports Mole's man of the match
Oscar: The Brazilian playmaker has been criticised for his lack of impact during the winter months, but he was back to his best on Tuesday evening. The 22-year-old always looked ready to create a chance for his team, while he was unlucky not to get on the score sheet on a couple of occasions. Chelsea will need him firing on all cylinders if they are to continue their run in the competition.
No major mistake stood out throughout the 90 minutes, but Galatasaray deserve criticism for their failure to show any kind of ambition during a laboured trip to England. Their fans displayed remarkable support, but their team failed to come close to rising to the occasion of a big European tie.
The fact that Felix Brych blew his whistle for 40 fouls throughout the match tells you everything that you need to know. The match was easy on the eye, but the official did his best to prevent any flow to the game. He was also guilty of handing a harsh caution to Oscar during the first half.
Chelsea: The Blues host Arsenal in a huge encounter at Stamford Bridge on Saturday before they travel to Crystal Palace seven days later.
Galatasaray: Galatasaray are left to concentrate on their pursuit of Fenerbahce in the Turkish Premier League, with five points currently separating the two sides.