Already leading 4-1 from the first leg, the Liga leaders ended up 9-1 victors across the tie on Tuesday, with two goals from James Rodriguez, one from Isco and an own goal by Borja Lopez preceding Jese's strike.
The Spaniard saw an impressive breakthrough season last term - which had led to calls for his inclusion in Spain's World Cup squad - cut short by a serious knee injury, but he hit the ground running on his return to action.
Carlo Ancelotti's side were almost embarrassed early on when Cornella midfielder Xavi Boniquet won his side a penalty.
Unfortunately for the third-tier part-timers though, the midfielder spurned the opportunity to give them a famous lead by blazing the spot-kick over the bar.
It would be the away side's one big chance, after which Real's superiority shone through to notch up a scoreline representative of the gulf between the sides.
With the tie effectively won previously and Cornella unlikely to pose any threat at the Santiago Bernabeu, Real coach Ancelotti opted to rest a host of his star names, including Cristiano Ronaldo, Karim Benzema, Toni Kroos and Sergio Ramos.
This gave an opportunity to the likes of Javier Hernandez, Asier Illarramendi and Sami Khedira to stake a claim for greater involvement in helping Real extend their recent faultless run.
However, there was an air of complacency about the home side in the opening stages, epitomised by Alvaro Arbeloa's lazy trip on Boniquet in the box, punished by referee Jose Gonzalez, but not the Cornella midfielder, who lifted his effort over.
The incident served as a wake-up call for the home side, who went straight down the other end and took the lead when Rodriguez latched on to a Isco's throughball and chipped over the advancing Inigo Alberto in Cornella's goal.
Though the Catalan visitors continued to compete, Real doubled their lead half an hour in as Isco matched the Colombia star's finish with a neat chipped goal of his own before Hernandez's flick set up Rodriguez to curl in his second a minute later.
As he had promised, Ancelotti brought on forward Jese in the second half - after Khedira was forced off with suspected concussion - for his first appearance since March.
The hosts' fourth arrived on the hour as a Hernandez chip came back off the bar and deflected in via the unwitting Lopez's shins, but the night's loudest cheer was reserved for their final goal.
Isco once again unlocked the Cornella defence with ease, allowing Jese to turn a low shot home and bring the Bernanbeu to their feet.
It was the final goal as Real extended their club-record winning run to 17 games in efficient if unspectacular fashion with home games against Celta Vigo in La Liga and Ludogorets in the UEFA Champions League to come as they approach 20.
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