Messi set up Luis Suarez for the opening goal before scoring a hat-trick as Ernesto Valverde's side made amends for their shock 5-4 defeat at Ciutat de Valencia last May.
The 31-year-old has now scored 50 goals for club and country eight times over the last nine calendar years and he helped round off the rout by setting up Gerard Pique for the fifth two minutes from time.
Barca's third straight LaLiga win put daylight between them, Sevilla and Atletico Madrid after 16 matches.
Levante were 2-1 up at half-time of this fixture last season and they caused Barca problems from the off once again, with Emmanuel Boateng, scorer of a hat-trick in that game, striking the underside of the crossbar from 12 yards.
But Barca made the most of Levante's failure to clear their lines 10 minutes before the break, when Messi danced his way across the top of the box and clipped a reverse pass into the path of Suarez, who volleyed home.
Three minutes before half-time, after another error, it was 2-0. Ruben Rochina passed straight to Sergio Busquets, he sent Messi through on goal and the Argentine star slotted the ball beneath Oier Olazabal.
Messi effectively killed the match before the hour mark, first sweeping into the bottom-right corner after Suarez and Jordi Alba led a counter-attack and then tapping in a first-time cross from Arturo Vidal.
Erick Cabaco saw a straight red card for a reckless challenge on Ousmane Dembele in the 76th minute, and Pique compounded a miserable outing for Levante in the closing moments, collecting Messi's pass, turning onto his left foot and squeezing a shot beneath Oier.
Valverde has learned his lesson
Valverde's decision to rest some key players, including Messi, in this fixture last season ended Barca's hopes of going the entire league campaign unbeaten.
This time, having already lost twice in LaLiga, there was to be no such risk. Even with Nelson Semedo withdrawing late on through injury, this was a strong line-up set up in a way to prevent being exploited on the break as badly as they were on their last visit.
Most importantly, he put Messi in the team, who was simply too much for the league's third-worst defence to handle. Barca now need only a point against Celta Vigo next week to guarantee they will end 2018 in top spot.
Messi a clinical colossus
Having come close with two efforts from distance, Messi showed his killer instinct to put the game to bed within an hour. His assist for Suarez and his three goals looked simple but oozed quality.
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