Two goals in the space of a minute from Ousmane Dembele put the Blaugrana in control of the match and ahead in the tie at half time. Lionel Messi then ensured the result was safe with a third after the break.
Elsewhere on Thursday, Espanyol made it through at the expense of Villarreal, with their 3-1 win at Cornella-El Prat seeing them to a 5-3 overall victory. Borja Iglesias was on the scoresheet twice for the hosts.
The big surprise of the round came in Atletico Madrid's elimination, as a 3-3 draw at the Wanda Metropolitano to Girona saw the underdogs through on away goals.
Copa del Rey Last-16 Results
Tuesday, January 15
Real Valladolid 1-1 (1-2) Getafe
Valencia 3-0 (4-2) Sporting Gijon
Wednesday, January 16
Atletico Madrid 3-3 (4-4) Girona
Leganes 1-0 (1-3) Real Madrid
Sevilla 0-1 (3-2) Athletic Bilbao
Thursday, January 17
Espanyol 3-1 (5-3) Villarreal
Barcelona 3-0 (4-2) Levante
The quarter-final draw will take place on Friday at 4 p.m. (GMT), per the Real Madrid website.
After losing the first leg of this tie, Barcelona manager Ernesto Valverde fielded a strong side for this clash with Levante, with Messi included in the XI.
The great man was able to knit passages of play together in the final third for his team and, as relayed by football journalist Rik Sharma, was involved in both early goals as Barcelona moved into a strong position to qualify for the last eight:
Meanwhile, Dembele continues to improve and has made an impression in all competitions this season for the team:
Having inspired Barcelona to a two-goal lead on the night, Messi was then able to get on the scoresheet himself after brilliant play from Nelson Semedo set him up for an easy finish.
Despite this victory Barcelona's position in the quarter-finals does appear to be in some doubt.
As reported by Goal, it's been stated that the Blaugrana fielded an ineligible player in Chumi during the first leg. Levante president Quico Catalan said the club will make a complaint to the Spanish Football Federation regardless of Thursday's result.
With healthy first-leg leads secured, both Real Madrid and Sevilla allowed their standards to slip in their follow-up fixtures.
Los Blancos boss Santiago Solari made numerous changes to his XI when Madrid travelled to Leganes. While the European champions were eventually only beaten 1-0, the hosts did have chances to cut the deficit further and make it a nervy evening for the capital club.
Following his recent marginalisation Isco was given a chance to shine from the start, although he struggled:
Sevilla were beaten by Athletic for the second game in succession, having lost to them in La Liga at the weekend, although there was never any real danger of the Basque side launching a comeback.
The clash of the round came at the Wanda Metropolitano, as there was drama in the latter stages of the match between Atletico and Girona.
When Antoine Griezmann put his side 3-2 up in the 84th minute on the night they appeared set to progress, only for Borja Garcia to equalise four minutes later and put Girona through.
It was the first time in his spell as Atletico Madrid manager that Diego Simeone had been involved in a game like this:
On Tuesday there was no drama for Valencia, as they easily overturned a one-goal disadvantage from the first leg against Sporting Gijon. Getafe were also well in control of their tie, when Angel Rodriguez's penalty in the first half meant Real Valladolid would need three goals to go through.