The Portuguese netted the opening goal at the 21st minute through a header at the right side of the six yard box, thanks to well-timed cross from left-back Marcelo to the streaking Ronaldo.
Goalscorers Ronaldo and Di Maria celebrating Real's triumph.
The match was dominated by Real, keeping possession at 58 per cent and attempting a total of 22 shots as opposed to København's 9.
But it was not until the 65th minute that Real found the back of the net again via another header, and this time, it's from Angel Di Maria's cross inside the box.
Di Maria joined the Ronnie-scoring party just five minutes after the second goal through a left-footed shot, just outside of the box, clinically placing the ball at the bottom-left corner.
Just when everybody thought it was over, Di Maria used his left foot again to beat København keeper Johan Wiland during added time.
Los Blancos boss Carlo Ancelloti was pleased with not only the result but with the way his team played to deliver such output.
"I think tonight we had more balance. The team was more compact and we tried to play deeper. The players followed the game plan we had prepared this week very well and the change in our attitude was very good," Ancelotti told uefa.com.
"We modified the system to use the flanks more and to create more open spaces. We had little space in midfield and that's why we made this change, because København are a very strong team. Our players have the quality to use all possible systems."
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