Carlo Ancelotti rested stars Cristiano Ronaldo, Karim Benzema, Toni Kroos and Sergio Ramos for the return leg at The Santiago Bernabeu but the European champions had no trouble disposing of Cornella as they won 9-1 on aggregate.
Real were almost embarrassed early on when Cornella midfielder Xavi Boniquet won a penalty, however he blazed his spot-kick over the crossbar.
That seemed to serve as a wake-up call for Real, who took a 16th-minute lead through James Rodriguez.
Isco doubled Real's advantage on the half-hour mark before Rodriguez netted his second of the match just minutes later.
Javier Hernandez - on loan from Manchester United - helped the home side bag their four goal in the 60th minute, with his chip deflecting into the net via some help from Borja Lopez's shins.
The scoring was completed 13 minutes from time, Jese Rodriguez capping his first match in nine months with a neat finish, as Real made it 17 successive wins in all competitions.
Real's fixture in Madrid was the only round-of-32 tie to be completed on Tuesday, with four first-leg matches getting underway.
La Liga outfit Athletic Bilbao were fortunate to escape Alcoyano with a last-gasp 1-1 draw.
Alcoyano, who ply their trade in Segunda B Group Three alongside Cornella - took a surprise 32nd-minute lead through Francis Ferron, who got his boot to a low shot across the six-yard box.
And just as Alcoyano appeared on track to record a famous win at the Estadio El Collao, Borja Viguera turned his defender inside the penalty area and fired a shot beyond goalkeeper Ignacio Zabal in the 90th minute.
Segunda Division outfit Las Palmas hold a slender advantage over top-flight side Celta Vigo after running out 2-1 winners.
Hernan and Marcelo Silva inspired the victory, with Santi Mina grabbing a late goal for the visitors via an 83rd-minute penalty.
There was no such trouble for Espanyol, who accounted for second-tier club Deportivo Alaves 2-0 away from home.
Real Valladolid and Elche played out a goalless draw, ahead of the latter's hosting of the second leg later in December.
