Without the injured Gareth Bale and suspended Cristiano Ronaldo, Real boss Carlo Ancelotti gave a number of his younger players another chance to impress despite being held to a 0-0 draw in the first-leg 10 days ago.
The Italian was rewarded as Asier Illaramendi slotted home his first goal for the club before Angel di Maria's penalty made it 2-0 at the break.
Madrid failed to add to their tally in the second-half, but were never threatened by their third-tier opponents as they eased into the next round where they will face Osasuna.
"I think we started the game well, but we slowed down when we were 2-0 up. Our rhythm dropped too much in the second-half and I didn't like it," said Ancelotti.
And the former Chelsea boss stressed that the likes of Jese Rodriguez and Alvaro Morata need to make the most of their opportunities in the absence of Ronaldo and Bale.
"It wasn't easy to prepare for the game because we changed the team a lot. Some players that haven't played a lot need more minutes to reach optimal condition.
"In general the young players need work because playing for Real Madrid is not easy. They need to be ready because this season we will need everyone, they need to be concentrated so that when the opportunity arrives, they take it."
Atlético Madrid, meanwhile, were forced to come from behind to beat minnows Sant Andreu 2-1 on the night at the Vicente Calderon to progress into the last 16, 6-1 on aggregate.
Alberto Carroza had fired the visitors into a shock lead as Atletico conceded for the first time at home since early October.
Atlético then passed up a host of chances to level before the break as Jose Gimenez had a goal harshly ruled out for offside, while Adrian Lopez blasted a penalty over the bar.
With such an advantage from the first-leg, Atlético boss Diego Simeone had handed a night off to the majority of his first-team regulars and had to turn to 18-year-old Hector Hernandez in his search for an equaliser.
The young forward duly delivered when he turned home Adrian's cross 12 minutes from time.
Sant Andreu looked like they may still hold out for a famous draw, but they were cruelly denied with the last action of the game as Toby Alderweireld headed home Gabi's free-kick deep into stoppage time.
Atletico will now face Valencia or Gimnastic in the next round.
Meanwhile, La Liga leaders Barcelona comfortably secured their place in the last 16 of the Copa del Rey with a 3-0 win over third-tier Cartagena , to seal a 7-1 win on aggregate.
Racing Santander produced the surprise of the evening as they overcame a 1-0 first-leg deficit with a 2-0 win away to 10-man Sevilla.
David Miguelez pulled the visitors level in the tie from the penalty spot after Stephane M'bia had been sent-off for hauling down Mariano Sainz inside the area.
Mahamadou Kone then sealed the comeback in stoppage time when he fired home from close range.
Real Sociedad set up a meeting with Villarreal in the last 16 with a convincing 4-0 win over Algeciras thanks to goals from Javi Ros, Haris Seferovic, Antoine Griezmann and Carlos Vela to seal a 5-1 aggregate victory.
La Liga sides Almeria and Real Betis also progressed despite being held at home on the night by lower league Las Palmas and Lleida respectively.