The Turkish champions had beaten Madrid on their visit to Istanbul in last season's quarter-finals and started the brighter of the two sides with Felipe Melo seeing a trio of efforts saved.
However, the Spanish giants were rarely troubled after Isco had fired them into the lead 12 minutes before half-time as they cruised to victory in the second-half thanks to two goals from Karim Benzema and three from Ronaldo with Umut Bulut's late strike the only consolation for the hosts.
"We couldn't have started better. To start in this manner gives us a lot of confidence," Ronaldo told TVE afterwards.
"We did our job against a very complicated opponent. Despite the result it was a difficult game.
"In the first few minutes they had their best chances. After our first goal we controlled the game and played well."
Real boss Carlo Ancelotti made Gareth Bale wait to make his European debut with the nine-time winners as he started on the bench before coming on for the final half hour.
However, it wasn't a happy evening for captain Iker Casillas as he had to be withdrawn just 15 minutes into his first appearance for the club in eight months due to a rib injury.
The Spanish international collided with teammate Sergio Ramos after just 60 seconds as he collected a routine cross into the area and, despite making one flying save from Melo, was in some discomfort as he came off to be replaced by Diego Lopez.
Melo then had two more fine chances to give the hosts the lead as he failed to make proper contact with Wesley Sneijder's free-kick before the Brazilian midfielder was denied by a brilliant save low to his left by Lopez.
Other than an Angel Di Maria shot that flew just over Madrid had barely threatened in the opening half hour, but they went ahead on 33 minutes when Di Maria's long pass picked out Isco and he controlled wonderfully before dispatching the ball into the net via the inside of the post.
Galatasaray keeper Fernando Muslera then had to be alert to keep his side in the game as he produced a fine double save from Di Maria and Ronaldo at the start of the second period.
Seconds later the hosts should have been level when Burak Yilmaz somehow headed wide from Nourredine Amrabat's cross.
And that miss was to prove costly six minutes later as two Galatasaray players went for the same long ball, only to present Di Maria with possession and he fed Benzema who finished calmly for his third goal of the season.
Ronaldo was the competition's top scorer last season with 12 and he finally got in on the act with two goals in little over three minutes just after the hour mark.
The Portuguese fired high into the net from point-blank range from Isco's headed cut-back and then volleyed home after Muslera could only parry Sergio Ramos' header from Bale's free-kick.
Ronaldo also played a key role in Madrid's fifth as he squared for Benzema to tap home his second of the evening from close range before Bulut restored some pride for the hosts with a deft finish of his own from Amrabat's cross.
And fittingly it was Ronaldo who was to have the final say with an incredible individual effort in stoppage time as he weaved past three Galatasaray defenders before smashing the ball high past the helpless Muslera.
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