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.
The Spanish champions were without the services of Lionel Messi - who was rested - and in-form Levante managed to hold off a late fightback from the visitors to collect all three points in spectacular fashion.
Barcelona boss Ernesto Valverde made five changes to the team that started against Villarreal on Wednesday night, with Marc-Andre ter Stegen, Yerry Mina, Jordi Alba, Ivan Rakitic and Luis Suarez all returning.
It did not take long for Barcelona to get to grips with their task as they dominated the early possession, and registered the game's first attempt in the second minute when Ousmane Dembele fired over the Levante crossbar from distance.
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.
The hosts should have doubled their advantage less than two minutes later when Boateng's shot found Enis Bardhi completely unmarked inside the Barcelona box, but the number 10 smashed the ball against the post.
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 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.
The Uruguay international should have levelled the scores moments later when he met a deep free kick from Denis Suarez, but the centre-forward's header missed the crossbar.
Levante managed to settle in the 10-minute period that followed, and were still threatening down the other end as Morales brought a save from Ter Stegen in the 81st minute.
Luna then almost turned into his own net seconds later as an incredible game continued to produce exciting moments.
Barcelona threw everything at Levante in the final stages as they looked to keep their long unbeaten run intact, 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.
LEVANTE (4-4-2): Oier; Coke, Postigo, Pier, Luna; Bardhi, Campana, Lukic, Boateng (Pazzini 77'); Morales (Rotchina 85'), Roger (Lerma 69')
BARCELONA (4-3-3): Ter Stegen; Semedo, Vermaelen (Pique 30'), Mina, Alba; Rakitic, Busquets, Iniesta (D. Suarez 60'); Coutinho, L. Suarez, Dembele (Alcacer 60')