Neymar opened the scoring on 34 minutes when Lionel Messi split the Levante defence open with a through-ball, and the Brazilian finished off the move by taking it past goalkeeper Jesus Fernandez and tapping it into an empty net.
With the first half drawing to a close, Barca doubled their advantage through Croatian international Ivan Rakitic.
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The former Sevilla star let fly with a powerful half-volley outside the box to put Luis Enrique's side firmly in the driving seat at the break.
A difficult evening for Levante got worse when Messi made it 5-0 with a chip over Jesus after the keeper had thrown the ball straight to the four-time Ballon d'Or winner.