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.
Earlier in the half, the home side nearly had the lead and Barca had Ivan Rakitic to thank when he cleared the ball off the line.
Neymar almost gave his side the opener on 25 minutes but his header glanced wide of the post after an excellent ball over the top by Javier Mascherano.
With the half drawing to a close, Barca doubled their advantage through Croatian international Rakitic.
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.