Karim Benzema netted inside two minutes, Jose Callejon doubled the lead four minutes later, Gonzalo Higuain made it 3-0 in the ninth, and Mesut Ozil rang up the fourth in the 20th as they made a whirlwind start at a rain-soaked Bernabeu.
Real's pace and aggression were too much for the Croatian champions and Callejon and Benzema scored again after the break.
Zagreb's Fatos Beqiraj scored the first goal against Real in Europe this season with a header in the 81st and Ivan Tomecak bundled in a second at the end as the hosts eased off.
Real's victory canter made it five wins from five in the group, and 12 on the trot in all competitions, putting them seven points ahead of second-placed Ajax Amsterdam.
"The game was decided in nine minutes," Real director and former player Emilio Butragueno told Spanish television.
"It was the first time Zagreb had played here, our first three attacks ended up as goals, it must have been traumatic for them.
RONALDO RESTED
"Madrid showed a great deal of confidence with many first choices out of the team and it hasn't affected our performance at all, so we are very pleased.
"The team is on a positive run and tonight proves the coach has a lot of players he can rely on which is a good sign."
Real coach Jose Mourinho, who rested Iker Casillas and Cristiano Ronaldo, handed Turkey midfielder Nuri Sahin his first start in midfield after an injury-delayed start to his Madrid career, and the hosts stormed into the lead.
Frenchman Benzema slotted home from Ozil's pullback after a swift passing move sliced open the visitors, and former Real youth team forward Callejon finished off a quick break.
Argentine Higuain cut inside his marker and then dinked the ball over the keeper at his near post, before Germany's Ozil put away a loose ball after Higuain's shot had been parried.
Callejon broke the offside trap to slot away number five in the 49th and Benzema made it 6-0 on 66 minutes.
As the game ran out of steam Beqiraj nodded in a neat goal, Benzema blasted an overhead-kick against the crossbar and Tomecak scored the visitors' second goal of the campaign.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
