
Hat-trick hero Thierry Henry was the star of the shown in Valencia, with his first goals in "La Liga".
Their third successive win gives Barca 14 points from six games, one point more than RealMadrid, who are away to lowly Getafe on Sunday.
In joint third place, on 12 points, are Villarreal and Valencia, who on Sunday face Athletic Bilbao and Recreativo Huelva.
"This was a really satisfying game," said Henry, who denied that he had been "obsessed" with scoring his first league goal.
"It doesn't really matter who scores," he added, "what matters is that we carry on playing well - and winning."
Henry opened the scoring in the 16th minute from close range, after nervous Levante goalkeeper Marco Storari had made a mess of a corner.
Seven minutes later Messi set up Henry to make it 2-0 with a cool finish.
The one-way traffic continued into the second half, and Henry sealed his hat-trick in the 48th minute by controlling a pass from Deco and scoring with ease at the near post.
The Levante defence was in tatters and it came as no surprise when Messi added a fourth just two minutes later. The in-form Argentine received the ball on the right, skipped majestically past two defenders and scored with his classy left foot.
Understandably, Barca eased up after the fourth goal, allowing Levante to come out of their shell.
In the 69th minute Levante striker Cristian Rigano hit the Barca post. A minute later the hosts were given a dubious penalty for a supposed foul by Carles Puyol on Alexandre Gijo.
Emilio Viquiera calmly put away the spot-kick, giving the Levante fans something to shout about at last.
Earlier on Saturday Zaragoza had beaten Sevilla 2-0, with second- half goals from substitutes Andres D'Alessandro and Sergio Garcia.
Their third successive league defeat leaves Sevilla in midtable and in something of a crisis.
DPA