The European champions lead Real Madrid, Villarreal and Celta Vigo by two points with Atletico Madrid a point further adrift in fifth.
Levante yesterday frustrated an experimental Barca side shorn of Luis Suarez from the start for 50 minutes before Marc Bartra settled the Catalans' nerves from Messi's cross.
The floodgates then opened as Neymar doubled the advantage before Messi converted his first effort from the spot.
Victor Casadesus pulled a goal back for Levante 24 minutes from time as he pounced on an error from Barca 'keeper Marc-Andre ter Stegen.
Messi then missed a penalty for the second time this season, but made amends with a stunning individual effort to round off the scoring.
"He isn't human because he scored two goals and provided an assist," Barca boss Luis Enrique joked when asked if Messi's struggles from the spot proved he is fallible.
"There is very little that makes him seem human." Suarez missed out on Enrique's starting line-up for the first time this season as he handed youngsters Sandro and Munir El Haddadi a rare start.
Yet, both failed to impress as Levante comfortably kept Barca at bay during the first period and could even have taken a shock lead had Nabil Ghilas kept his composure instead of blazing wildly off target midway through the half.
In the absence of Suarez and Andres Iniesta, Messi was playing in a deeper midfield role and it was his creativity that eventually undid Levante as Bartra controlled the Argentine's inch-perfect cross before slotting past Ruben Martinez.


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