The Spanish giants stormed into a 3-0 lead over Dinamo Zagreb inside nine minutes with goals from Karim Benzema, Jose Callejon and Gonzalo Higuain, and Mesut Ozil made it four before 20 minutes were up.
Callejon and Benzema struck again after the interval and Madrid could have had even more goals, while late strikes from Dinamo's Fatos Beqiraj and Ivan Tomecak gave a merely cosmetic effect to the scoreline.
The opener came after just 83 seconds as Benzema tucked away Ozil's cut-back to round off a flowing team move.
The France striker then laid the ball off for Callejon to rifle home the second from the edge of the box and there were still only nine minutes on the clock when Higuain netted a delicious third.
Racing into the right side of the penalty area, the Argentinian flummoxed defender Leandro Cufre with a sharp turn before producing a deft finish over wrong-footed keeper Ivan Kelava.
Higuain then fired Fabio Coentrao's cross over the bar before Luis Ibanez had shell-shocked Dinamo's first real effort, curling a free-kick over.
Benzema was off target from distance but Real's fourth was not long in coming, Ozil finishing calmly after Kelava parried Higuain's drive.
Kelava remained defiant in the face of the onslaught, saving with his feet to deny Coentrao and then tipping Benzema's shot over.
Dinamo sought to get themselves on the scoresheet as half-time approached but Jorge Sammir fired over after Benzema only half-cleared Mehmed Alispahic's corner and Ibanez then shot straight at keeper Antonio Adan.
But, after making all three substitutions at half-time, Madrid quickly extended their lead as Callejon latched onto Raphael Varane's long ball and was allowed to finish too easily inside the near post.
Kelava was fighting a lone battle at times and did well to tip efforts from Higuain and Callejon around the post in quick succession.
But he was left helpless when Benzema took Higuain's pass, waltzed through two weak challenges and found the bottom corner of the net.
Beqiraj had one effort blocked by Raul Albiol but was not to be denied, heading home Ibanez's cross for his side's first goal of the tournament - and the first conceded by Jose Mourinho's side.
Benzema hit the bar and drew another sharp save from Kelava as he chased his hat-trick, and substitute Hamit Altintop had a shot blocked, but it was Dinamo who had the final word as Tomecak turned in Milan Badelj's cross.