Here, Sports Mole takes a closer look at how the action unfolded in Spain.
On target 4
On target 5
Was the result fair?
For a team playing with 10 men, this was as good as it gets from Real Madrid. They made Galatasaray look like they had seen an important defender dismissed, and the home side could have easily netted a couple more goals. The Turkish side did well at times, but they always looked like conceding goals.
Real Madrid's performance
With Cristiano Ronaldo, Xabi Alonso, Luka Modric and Karim Benzema missing from the starting lineup, there was a danger that Real Madrid could struggle to create chances this evening. However, after losing Sergio Ramos, they played with a freedom in attack, and with Gareth Bale always offering an outlet, they frequently looked capable of goals.
Galatasaray will be desperately disappointed not to take anything from the game after keeping the score level for 50 minutes. They replied almost instantaneously after Bale's opener, but as soon as Arbeloa netted the second, they were always chasing the result and more holes began to appear at the back.
Sports Mole's man of the match
Alvaro Arbeloa: This might be a surprising choice to some, but the former Liverpool man was hugely influential in Real's win tonight. He popped up with the second, contributed to the third, and could have helped himself to an unlikely hat-trick. It's unlikely that he will ever play such a big part in attack as this, so the Spaniard get tonight's accolade.
Although it didn't cost his side, Sergio Ramos made the biggest gaffe of the night by being sent off early on. It was a challenge that he didn't need to make, but with his track record of red cards, it was unsurprising that he opted to pull back Umut Bulut.
Scot William Collum had a solid game in his appearance at the Bernabeu, but he was wrong to harshly book Arbeloa after the full-back was tripped in the penalty area. Other than that, Collum made very few errors and he didn't have an impact on the result.
Real Madrid: With their passage through to the second round confirmed, Real can concentrate on domestic action, beginning with their fixture against Real Valladolid on Saturday.
Galatasaray: Given that they are currently sitting in fifth position in their domestic league table, Galatasaray can't afford to ease off for two weeks ahead of their clash with Juventus. I'm sure that Roberto Mancini will be looking to build up some momentum ahead of that fixture.