It meant a 10-1 aggregate triumph over its third-tier opponent to progress to the last 16, with Marco Asensio's quickfire double after the half-hour getting Madrid up and running.
Asensio then crafted a maiden senior strike for rookie centre-back Javi Sanchez, with Isco – making his first start under Solari – netting brilliantly in the 47th minute.
Vinicius Junior got in on the act and Isco's second came after Yacine Qasmi converted a consolation penalty for the visitor.
Mohamed Mohamed Mahanan needed a brilliant last-ditch challenge to deny Mariano as Madrid predictably started quickly and Vinicius blazed over after clever work from Isco.
It left Asensio to show his team-mates how it should be done as he eased through an already-tiring defence in the 33rd minute and caressed a finish past Pedro Luis.
Right-back Pepe Lopez was beaten far too easily by Vinicius, as he set up a second for Asensio, who then turned provider with a chipped pass for Javi Sanchez to volley in off the underside of the crossbar.
Isco spectacularly got in on the act early in the second half, clipping a brilliant 25-yarder into the top corner – earning Solari's applause as the Bernabeu faithful sung his name.
There was less to shout about for Vinicius, who rounded Pedro Luis but could only bundle a finish into the side netting before the goalkeeper repelled a later strike with his feet.
Persistence paid off for the 18-year-old, who unfurled a celebratory jig in the 75th minute after beating Pedro Luis at the second attempt.
Javi Sanchez blotted his afternoon with the foul that allowed Qasmi to send Keylor Navas the wrong way before Isco was given space to lash into the bottom corner from 10 yards in the 83rd minute.