Barca won last week's first leg 4-1 thanks to Cristian Tello's hat-trick, all set up by Lionel Messi.
As they did that night, Levante took the lead in the second leg when Loukas Vyntra's wayward header cannoned in off the unlucky Sergi Roberto for a ninth-minute own goal - but again Barca surged back at a rain-drenched Nou Camp.
Adriano's wicked curling, dipping finish left keeper Javi Jimenez helpless and Carles Puyol headed in Tello's corner a minute before half-time.
At 6-2 with 45 minutes to go, the tie was well and truly over, and when Alexis Sanchez tapped in Barca's third of the night after Jimenez fumbled Martin Montoya's tame shot, it was a question of how many.
Sanchez immediately netted an equally simple fourth, Jimenez unlucky this time after diverting Adriano's deflected shot onto the crossbar, and Cesc Fabregas completed the scoring via another deflection immediately before being substituted.
Barca will face the winners of the last tie to be completed, with Real Sociedad holding a 3-1 advantage against Racing Santander going into Thursday's second leg.
Earlier, Atletico Madrid completed a 3-1 aggregate win over Athletic Bilbao by winning 2-1 at San Mames to set up a tie against Real Madrid.
Mikel Balenziaga crossed for Aritz Aduriz to head Bilbao in front on the night and cancel out Diego Godin's first-leg goal, but Raul Garcia swept home for Atletico 10 minutes after half-time.
That would ultimately prove the decisive goal in the tie, though Diego Costa ran clear to add to the margin of victory four minutes from time.