Ronaldo, top scorer in the competition, took his goal tally for the season to 11 to make sure that Jose Mourinho's side went through to the last four 5-3 on aggregate despite losing the second leg 3-2 in Istanbul.
Mourinho praised the passionate support generated by the home crowd and the spirit of the Galatasaray players.
"We always want to play in an atmosphere like the one in the stadium tonight," he told reporters. "I don't think our players were affected by it but the Turkish players were really affected.
"They used the atmosphere in the second half and played a fantastic match. They were knocked out but if only all clubs would go out in the same fashion - they put their heart and pride into it."
Didier Drogba, Chelsea's hero in last year's final, then sent the noisy crowd into raptures with a delightful backheel following a cross by substitute Nordin Amrabat.
Real substitute Alvaro Arbeloa was sent off in the closing stages for a second caution but Ronaldo settled his team's nerves by adding his second goal in stoppage time after good work by Karim Benzema.
The Madrid team, who romped to a 3-0 win in the first leg at the Bernabeu, were in complete command after Ronaldo's seventh-minute goal in Istanbul.
At the start of the second half nine-times European champions Real appeared content to sit on their lead but Eboue's goal transformed the atmosphere and it sparked a period of sustained pressure from the home team.
Sneijder dragged his shot well wide when he was unmarked eight metres out before the Dutch international struck Galatasaray's second goal.
