Cristiano Ronaldo netted a double for the Spanish champions but his goals book-ended a trio of fantastic efforts from Gala who gave themselves every chance of turning around the three-goal first leg deficit before Madrid won 5-3 on aggregate.
Ronaldo opened the scoring in the seventh minute, making it 4-0 overall, when he turned home Sami Khedira's low cross to give the visitors complete control.
In the 71st minute, Wesley Sneijder made it 2-1 to Gala when he produced a neat first touch from Sabri Sarioglu's brilliant through ball before firing past Diego Lopez before Didier Drogba added a third just a minute later with a delightful backheel from Nordin Amrabat's cross from the right which had Lopez scrambling.
As Gala piled forward in search of more goals, Ronaldo netted his 48th goal of the season with a customary finish from the centre of the area from Karim Benzema's cross in injury-time, minutes after Alvaro Arbeloa was sent off for a second bookable offence.
The victory enables Madrid to move through to the final four of Europe's premier club competition giving manager Jose Mourinho seven semi-finals out of the last 10 seasons.
2012/13 UEFA Champions League - quarter-final second leg
Turk Telekom Arena, Istanbul - 49,975
Red card:RM - Alvaro Arbeloa 90'