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Yamal struck twice, in the 19th minute and again from the penalty spot in the 48th, after young full-back Xavi Espart had given the reigning champions an early lead in the fifth minute. German substitute Karim Adeyemi added a fourth in stoppage time (90+2).
Levante hit back through substitute Iván Romero and Roger Brugué, who found the net in the 79th and 88th minutes respectively, setting up a nervy finish.
The win lifted Barcelona to 15 points at the summit, three clear of arch-rivals and closest challengers Real Madrid on 12. The Catalans have now scored 21 goals in five matches, an average of more than four per game.
It was also Barcelona's fifth straight league win and their sixth overall from six matches across all competitions, following their emphatic 5-1 victory over Dutch side Feyenoord in their opening Champions League fixture.