Fresh from walking away with the FIFA Ballon d'Or award on Monday, Ronaldo netted with his first attempt on target in the second leg of the last-16 clash with Osasuna as 10-man Real won 2-0 on the night and 4-0 on aggregate, although his 21st-minute strike came courtesy of a calamitous error from goalkeeper Andres Fernandez.
Ronaldo fired a dipping 30-yard free-kick over the wall and Andres attempted to punch it clear, only to see the ball bounce down between his legs and he scrambled in vain to prevent it from rolling over the line.
Angel Di Maria doubled Real's advantage nine minutes into the second half after rifling home Jese Rodriguez's cut-back following a lung-busting surge down the right flank.
Cejudo hit the outside of the post with a low curling effort from the edge of the penalty area in between Real's goals as Osasuna briefly threatened to make a game of it.
Fabio Coentrao endured a nightmare return from two months out injured as he was shown a second yellow card late on for a needless kick at Oier.
Next up for Real – who extended the club's unbeaten run in competitive matches to 16 games – are Espanyol in the last eight.
Espanyol overturned a first-leg deficit against Alcorcon - going through 4-3 on aggregate after a 4-2 win.
The Segunda outfit put their opponents in real danger in the opening five minutes as Oscar Plano found the net to register a vital away goal and put the upset within touching distance.
However, Espanyol battled back through a Simao strike and a Sergio Garcia spot-kick to give themselves a fighting chance of progressing.
Javito levelled the game to give Alcorcon hope with 10 minutes to go, but Victor Alvarez and Pizzi struck within three minutes of each other to end the second-tier side's charge.
Athletic Bilbao progressed thanks to a 2-0 win over Real Betis at San Mames, having lost the first leg 1-0 in Seville.
Bilbao cancelled out Betis' lead from the opening leg when Mikel Rico stroked home after receiving the ball from Andoni Iraola in the 23rd minute.
Tempers briefly flared as the players left the field for half-time, before Rico doubled Bilbao’s advantage in the 76th minute with a deflected effort into the bottom right-hand corner of the net to put the hosts into the final eight - where they will face holders Atletico Madrid.
Levante appear on a collision course with Barcelona – who play Getafe on Thursday with a 4-0 first-leg lead – after David Barral scored the only goal of his side's tie with Rayo Vallecano.
