Zinedine Zidane's side led 3-0 from the first leg, meaning they were were hot favourites to progress and duly obliged, although Numancia's late equaliser ensured it was a fairly embarrassing result at home to lower-division opposition.
Real Madrid's healthy first-leg lead allowed manager Zinedine Zidane to make wholesale changes to his starting lineup.
The Frenchman made 10 changes from Saturday's La Liga draw with Celta Vigo, and the team was shared by the club's official Twitter account:
Despite all the changes, Real Madrid took just 10 minutes to open the scoring as Dani Carvajal crossed for Vazquez to head home unmarked at the far post.
Squawka Football showed how much Vazquez seems to enjoy playing in the Copa del Rey:
The goal was a real blow to Numancia who had seen some bright moments but lacked the quality in attack to trouble goalkeeper Kiko Casilla.
Madrid, meanwhile, were seeing plenty of the ball, but with the game already safe, they seemed to lack the drive and desire to add to their tally.
The hosts were then shocked on the stroke of half-time when Numancia equalised through Guillermo Fernandez Hierro.
Marc Mateu was played in down the left and crossed for Guillermo, who had just come on as a substitute for the injured Higinio Martin, to head first time past Casilla.
ESPN FC's Dermot Corrigan noted the home fans were not too impressed with the half-time score:
The hosts looked far brighter after the break, with Vazquez firing a chance just over the bar before restoring Madrid's lead on the hour mark.
Marco Asensio surged down the right before crossing for Borja Mayoral to head back to Vazquez to acrobatically fire home.
Opta showed how it was Vazquez's first double for Los Blancos:
However, Numancia continued to threaten and managed to grab a leveller with just eight minutes of normal time remaining, when Guillermo got on the end of a great cross from Saul and headed past Casilla.
The goal set up an intense end to the game as both teams looked for the winner, and Numancia saw centre-back Dani Calvo sent off after picking up a second yellow card for a foul on Isco.
However, the visitors hung on for a deserved draw and departed the Bernabeu as the happier of the two sides, despite exiting the competition.
For Madrid, it was another less-than-convincing display, with Zidane's fringe players doing little to suggest they deserve more time in the first team.