Lionel Messi celebrated scoring on his 400th appearance for Barcelona.
Ousmane Dembele was making his first La Liga start since September after suffering a horrendous hamstring injury which required surgery.
Messi was making his 400th appearance for the Catalan outfit and celebrated it in style by ghosting into the box and finishing offjdordi Alba’s knock-down on the half-volley.
Luis Suarez then finished off a patient move eight minutes before the break by thumping a volley home from Sergi Roberto’s cross.
Ivan Rakitic flashed a shot wide just before the break as Barcelona completely over-powered their visitors.
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Barca had a strong penalty appeal turned down nine minutes after half-time when Shaquell Moore slid into Alba in the area.
Moore was then involved at the other end as he had Levante’s first clear chance of the game but he was denied by the feet of Marc-Andre ter Stergen.
Dembele was withdrawn 20 minutes from time to ensure he did not burn out on his return from action.
Paulinho added the final goal deep into added time after playing a one-two with Messi.
The win ensures Barcelona go back to nine points above second-placed Atletico Madrid, who beat Getafe 2-0 yesterday.