Barcelona, who went into the game needing a win to keep their unbeaten record in the 2017/18 Laliga season intact, suffered an early blow as Ghanaian hitman Emmanuel Boateng netted in the 9th minute after firing a perfect shot past goalkeeping Ter Stegen.
The defeat is Barcelona's first in the league since April 2017, with a hat-trick from Emmanuel Boateng helping Levante make it eight wins from their last 10 top-flight matches.
Levante incredibly took the lead in the ninth minute, however, when Boateng turned a Jose Luis Morales cross into the back of the net from close range.
Dembele had one deflected wide of the home side's goal in the 25th minute as chances continued to arrive at either end, but it was Levante that scored the game's second goal on the half-hour mark.
An injury to Thomas Vermaelen disrupted Barcelona's defence, and Boateng took advantage of the uncertainty as the forward broke into the box before rounding Ter Stegen and finishing into the back of the net from close range.
Barcelona halved the deficit in the 38th minute, however, when excellent work from Gerard Pique ultimately found Philippe Coutinho in space, and the Brazilian's powerful strike from distance found a route past Oier.
Levante scored their third less than one minute into the second period though, with Bardhi picking out the top corner in spectacular fashion to stun Barcelona once again.
Three minutes later, Levante had their fourth of the match when Antonio Luna broke forward before feeding Boateng, who found the far corner in true style to complete his hat-trick.
The hosts then made it 5-1 in the 56th minute, with Bardhi finding the top corner once again after being picked out by Roger inside the Barcelona box.
Coutinho had one back for Barcelona just before the hour when he smashed home following a mix-up inside the Levante box, and Denis Suarez and Paco Alcacer were introduced shortly after.
Coutinho completed his hat-trick in the 63rd minute when he found the far corner with a wonderful strike from distance, and the comeback was very much on for the away side.
Luis Suarez scored Barcelona's fourth when he converted from the penalty spot following a rash challenge from Boateng on Sergio Busquets.
Barcelona threw everything at Levante in the final stages as they looked to keep their long unbeaten run in tact, but it was the home side that had the best chance to score the game's 10th goal - Ruben Rochina somehow firing wide from close range following a mistake from Busquets.