Denied by the hosts in the first half yesterday, Messi withdrew into midfield to turn playmaker and place four precise passes behind the defense that led to an own goal in the 53rd minute and Tello's treble in the 60th, 81st and 86th.
Levante had held Barcelona to a 1-1 draw at Ciutat de Valencia Stadium just four days earlier in the Spanish league, and it was on course toward a similar feat after Nabil El Zhar netted in the 31st.
"It's spectacular to have a player like Messi on your side," said Tello.
"All four goals came from his boots."
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Elsewhere, Real Sociedad defender Mikel Gonzalez scored twice to help earn a 3-1 victory at home over third-division Racing Santander in their opening leg.
Levante found Barcelona's weak spot in defending set pieces when Carles Puyol's clearance of a free kick fell for El Zhar to score at the second attempt after goalkeeper Jose Pinto had blocked his powerful first shot.