Substitute Kaka sparkled and Karim Benzema scored twice as Real Madrid finally broke down Cypriot underdogs Apoel in Nicosia.
The Brazil international was introduced in the 63rd minute and set up Benzema for a 74th-minute opener before tucking away fellow sub Marcelo's excellent cutback eight minutes later.
France striker Benzema's second gave the scoreline an emphatic look despite a mighty defensive effort by Apoel, whose giant-killing run has accounted for Lyon, Porto and Shakhtar Donetsk but who were outclassed tonight.
Apoel lost key defender Marcelo Oliveira to injury inside 10 minutes after his standing leg twisted under him as he overcommitted in a tackle.
Mesut Ozil tested goalkeeper Dionisis Chiotis, with the hosts still down to 10 men before replacement centre-half Kaka - the namesake and compatriot of Real's in-form schemer - could be introduced.
Fabio Coentrao shot well wide and a frustrated Cristiano Ronaldo was beckoned to his feet by referee Felix Brych after tumbling over Savvas Poursaitidis.
Benzema was guilty of a shocking miss in the 33rd minute when he hung a foot out at Ronaldo's low cross but stubbed the ball into the ground and it bounced over the bar.
Ronaldo sliced wide when picked out by Ozil as Real were held at bay until the interval.
Benzema lashed over from the edge of the box early in the second half and Ronaldo was similarly inaccurate before another Benzema effort was blocked.
Ailton lifted the home crowd with a wonderful solo run down the left before being fouled by Sergio Ramos, but the free-kick came to nothing.
Jose Mourinho was driven to a double change in an attempt to lift Real, introducing his own Kaka and Marcelo for Higuain - injured a few minutes previously - and Coentrao.
Esteban Solari, the brother of former Real stalwart Santiago, stepped off the APOEL bench - but soon found his side trailing as the better-known Kaka crossed deliciously from the left and Benzema dived to head past Chiotis.
The keeper saved Ronaldo's drive with his legs and then fumbled Kaka's effort as Real sought a killer second goal.
And it duly arrived as Marcelo was caught in the box by Paulo Jorge but kept his balance and cut the ball back for Kaka to slot home.
Benzema tucked away Ozil's inviting low pass in the last minute as Real put the tie to bed ahead of April 4's return leg.