The Catalan giants came from behind to virtually book their spot in last four of the competition thanks to Tello's masterful display on Wednesday.
All three of his goals were assisted by Argentina star Lionel Messi, who was typically excellent for Barcelona.
The two sides played each other in La Liga on Saturday, and Gerardo Martino's men were frustrated in a 1-1 draw.
They fared much better on this occasion, but Pedro's early chance saw him hit the post in the eighth minute.
Levante took the lead just after the half-hour mark as Nabil El Zhar thrashed home a loose ball.
It gave Joaquin Caparros' side the lead at half-time, but Barcelona were brilliant after the break as Tello and Messi took control.
They levelled proceedings in bizarre circumstances, as Loukas Vyntra's attempted clearance hit Juanfran and bounced into the bottom corner, leaving goalkeeper Javi Jimenez stranded.
Messi's angled pass then sent Tello through on goal and the young forward made no mistake with his right foot in the 60th minute.
Tello's assured finishing was again on display when he netted his second with nine minutes left, and there was still time for him to score his third, converting a delightful chipped Messi ball with another strike.
Barcelona now have the luxury of resting players during the second leg at Camp Nou on January 29.
In Wednesday's other match, Real Sociedad beat Racing Santander 3-1 to take the initiative into the second leg.
Mikel Gonzalez opened the scoring in the fourth minute for the victors, and he added another 12 minutes before the break.
Former Arsenal forward Carlos Vela wrapped up the result on the night in the 62nd minute, but a late goal for Santander's Mamadou Kone gave them hope ahead of the return clash.
