With just nine minutes on the clock, the away side took the lead as Loukas Vyntra powered a header into the bottom corner of the Barca net, though the ball took a deflection off midfielder Sergi Roberto.
Ten minutes later, Roberto came close to pulling a goal back for the Blaugrana, but Javi Jimenez pushed his effort over the crossbar.
Just as it seemed that both sides would be going in level at the break, Carles Puyol powered a header into the Levante net following a corner.
It would prove to be all one-way traffic after the break, as Alexis Sanchez scored two goals in as many minutes early on in the second half to bring the scoreline to 4-1 on the night.
Just before the hour mark, Marc Bartra attempted a bicycle kick in the Levante box, but Vyntra did just enough to thwart him.
Eight minutes later, however, the fifth Barca goal came, courtesy of Fabregas. He struck from inside the box after some good work by Sanchez.
This would prove to be his last action of the game, as he was then substituted by Ibrahim Afellay.
Barcelona will now face either Real Sociedad or Racing de Santander in the last four.