Neymar opened the scoring, with Messi adding the second in the 38th minute as Barcelona looked totally comfortable against their lowly opponents.
The Argentina striker added his second and Barcelona’s third in the 59th minute as Luis Enrique’s side continued to dominate the match.
Messi then completed his hat-trick from the penalty spot in the 65th minute before Luis Suarez added the gloss with a fifth goal courtesy of a bicycle kick.
The win means Barcelona are now back to within a point of Primera Division leaders Real Madrid, who defeated Deportivo La Coruna 2-0 on Saturday.
Messi was key in four of Barcelona’s goals – creating the first for Neymar before scoring a hat-trick himself.
The home side dominated the match throughout and claimed an early lead when Messi found some space after cutting inside before finding the run of Neymar at the back post, who took the ball first-time on the volley to loop it over Levante keeper Diego Marino in the 17th minute.
Messi then handed the home side a 2-0 cushion before the break when defender Marc Bartra won the ball in midfield then released the striker, who made no mistake with a low strike into the bottom corner.
Messi squandered the chance to put Barca 3-0 up ahead of half-time when he opted to shoot from the edge of the box instead of playing in Brazilian Neymar, who was totally unmarked a few yards out. Messi’s shot went wide but the home side were well in control.
The diminutive striker was on target, though, just before the hour mark to wrap up victory for his side when Sergio Busquets chipped a pass over the Levante defence, where Pedro was waiting to lay a volley into the path of Messi, who slotted his second.
Neymar then won a penalty when he was brought down by Levante right-back Ivan Lopez, with Messi stepping up to fire in from the spot to complete his hat-trick.
Barcelona did not take their foot off the gas, with Suarez claiming their fifth goal in the 73rd minute when he was on hand in the middle of the box to bicycle-kick Adriano’s pull back from the byline past Marino.
Messi was denied his fourth by Marino five minutes from the final whistle when the Levante keeper tipped his left-footed half-volley over the bar.