Gerardo Martino's men were held to a 1-1 La Liga draw at Levante on Sunday but stayed top on goal difference after Atletico Madrid also dropped points, with Real Madrid a point further back.
Loukas Vyntra put Levante ahead in the 10th minute, but Gerard Pique earned Barca a share of the spoils with his first league goal of the season.
However, Barca are the most successful team in the competition's history, with 26 triumphs, and have conceded just once in their four Copa del Rey outings this season, comfortably beating Cartagena and Getafe home and away.
When the sides met earlier in the Liga season, Diego Simeone's men ran out 2-0 winners and will be expected to reach the last four.
A repeat of last season's final will happen in the semi-finals if Atletico can defeat Bilbao and Real Madrid progress past Espanyol.
Carlo Ancelotti's side travel to Estadi Cornella-El Prat on Wednesday, a ground they won 1-0 at on January 12.
Pepe grabbed the only goal of that game and Madrid have since continued their impressive form with wins over Osasuna in the Copa del Rey and Real Betis in the league, thrashing the latter 5-0 on Saturday.
Santander beat Almeria in the previous round and also knocked out Sevilla.
Next up are out-of-sorts Sociedad. The Liga side have won once in their last four games to hamper the club's top-four hopes.
