The victory has seen Barcelona move three points clear of second-placed Sevilla at the top of La Liga, while Levante remain down in eighth having lost for the sixth time in the league this term.
Emmanuel Boateng, who scored a hat-trick against Barcelona in the corresponding match last term, had the first chance of the match in the fifth minute, but the striker could only fire straight at German goalkeeper Marc-Andre ter Stegen.
Barcelona's first sight of the Levante goal arrived in the 10th minute when Messi worked some space in a forward area before looking to pick out the bottom corner, but the ball missed the post.
Boateng was also involved in Levante's next half-chance in the 21st minute, with the striker just failing to meet a cross from Jason during a period where both teams were having their moments in the final third.
Boateng had another opportunity in the 34th minute when the ball broke kindly for the number 21 inside the Barcelona box, but the crossbar came to the away side's rescue.
Less than one minute later, Barcelona were ahead. The goal stemmed from Enis Bardhi conceding possession in a dangerous position, and Messi's excellent cross was volleyed into the back of the net by Luis Suarez for 1-0.
The home side impressed for long stages of the first half, but were undone by two excellent goals as Barcelona took a huge step towards securing another three points.
If the match was not over at the interval then it was shortly after the break, with Messi scoring his second in the 47th minute by sweeping a low cross from Jordi Alba into the bottom corner.
Oier did well to keep out Luis Suarez in the 56th minute, but Barcelona had their fourth in the 60th minute when Arturo Vidal's low cross was turned home by Messi to complete his hat-trick.
Arthur tested Oier from distance in the period that followed as Barcelona looked for more goals against a team that were simply shell-shocked by the Spanish champions on the night.
Bardhi fired just wide of the Barcelona post in the 74th minute, but any slight hint of a late comeback ended in the 77th minute when Erick Cabaco was handed a straight red card for a poor challenge on Dembele.
Luis Suarez missed a golden chance for 5-0 as he slid past the post 10 minutes from time, but Levante were also having opportunities, with Ter Stegen forced to keep out a low strike from on-loan Real Madrid forward Borja Mayoral.
Barcelona had their fifth in the 88th minute though when Gerard Pique, who had ventured forward after regaining possession in a defensive position, squeezed the ball home from close range.
Mayoral had the ball in the back of the net for Levante in stoppage time, but the offside flag came to Barcelona's rescue as the Spanish champions posted another clean sheet.
LEVANTE (3-4-3): Oier; Pier, Postigo (Prcic 70'), Cabaco; Jason, Bardhi, Campana, Tono; Rochina (Coke 69'), Boateng (Mayoral 62'), Morales
BARCELONA (3-4-3): Ter Stegen; Vermaelen (Arthur 52'), Pique, Lenglet; Alba, Busquets, Vidal, (Coutinho 78') Rakitic; Dembele (D Suarez 82'), L Suarez, Messi