Published: 2019-01-11 04:46:34 BdST
Barca, who have won the last four editions of the Spanish Cup, fell behind in the fourth minute when slack marking from a free kick saw Erick Cabaco head home while Borja Mayoral, on loan from Real Madrid, doubled Levante's lead in the 18th.
Substitute Jose Luis Morales spurned a glorious chance to strike a third goal for the home side which would have seriously damaged Barca's hopes of staying in the competition.
But the Catalans were handed a huge boost heading into next Thursday's second leg at the Nou Camp when Denis Suarez was fouled in the penalty area and record signing Philippe Coutinho converted the resulting spot-kick in the 85th minute.
The Argentine was left out of the squad along with usual strike partner Suarez and Ivan Rakitic, Gerard Pique and Jordi Alba, although regulars such as Ousmane Dembele, Arturo Vidal Sergio Busquets and Brazilian Coutinho all started the game.
Barca's out-of-favour Brazilian forward Malcom missed two clear chances in the first half after Levante's bright start, while French winger Ousmane Dembele dazzled the home defence in the second half but fell over just as he was shaping to shoot.
Barcelona's Denis Suarez was one of three players thrown on by Ernesto Valverde and the midfielder, linked with a move away from the club this month, earned the penalty which Coutinho netted to boost the chances of turning the tie around next week.