The Argentine's stunning volleyed opener was matched for style by his Uruguayan counterpart, who lashed home to finish off a direct Barca attack which included a pinpoint first-time cross via Sergi Roberto before the frontman's two-touch finish.
The convincing victory, Barca's 15th of the season in the top-flight, was eventually rounded off by Paulinho, who tapped home from close range.
The result leaves Barcelona still head and shoulders above the rest in La Liga, while Levante still hover just three points above the drop zone on their return to the Spanish top-flight
It was a rather unprecedented start inside the fan-pepped Camp Nou, with the early attacking initiative taken by the visitors through midfielder Cheick Doukoure, who found himself in an unusual striking role within an experimental Levante lineup, and caused the hosts' defensive line a number of problems.
But despite finding themselves under the cosh in the opening moments, Barcelona did not take long to find the breakthrough, and once again it was through Messi, who was making his 400th league appearance, via Jordi Alba.
The Argentine scooped play to the Spaniard on the left-hand side before receiving possession back through a looped header, which the 30-year-old met on the volley and powered his effort into the corner past the helpless stretch of Oier Olazabal to mark the fifth occasion this term where the duo's link up had resulted in finding the back of the net.
The Barca favourite's first of the calendar year and 16th of the season seemed to spark the hosts into action, and had it not been for the combination of the Levante custodian and defender Antonio Luna, either Luis Suarez or Ousmane Dembele, who was making his starting debut at the Camp Nou following a long layoff, could have doubled the lead moments later.
Messi danced past his opposite number on the left-hand side before squaring his pass across the face of goal, which the Uruguay international met unopposed, but his shot was straight at the goalkeeper.
The 28-year-old's smart stop did not alleviate the danger fully, however, as Dembele latched onto the subsequent rebound, but could only find the legs of Luna, who eventually guided the ball away to safety.
After failing to find their second of the afternoon, the hosts could have been pegged back to level terms as Doukoure found space on the edge of the area, but the Ivorian skewed his effort wide.
Following a couple more sightings of goal for Levante, it was the Catalonians turn to spurn a goalscoring opportunity, as Dembele's stinging attempt from the edge of the area was parried into the direction of the advancing Suarez, however, the 30-year-old lashed his effort over the bar from a relatively tight angle.
But the Uruguayan did not take too much longer to get off the mark in 2018, and he did so in spectacular fashion
Javier Mascherano lofted his pass from deep to the surging Sergi Roberto on the right-hand side, whose simply magnificent first-time cross found Suarez, and following a controlling touch, the frontman blasted his shot into the top left-hand corner, leaving Olazabal stranded and doubling his side's advantage.
It could well have been three as half-time approached, with Ivan Rakitic coming inches away from goal following his long-range volleyed effort, but as it was the Catalan's lead remained two going into the break.
Similar to the first, the second 45 started with Levante on top, with Marc-Andre ter Stegen forced into a sublime save inside the opening minute following Ivan Alvarez's rifled attempt after some impressive trickery to work a pocket of space for himself on the edge of the Barca area.
As the half trickled on Barca continued to struggle to get themselves back to the levels they had reached during the opening stages, and following the hour mark, the German custodian was forced into his second good save of the afternoon.
The move started with the visitors' captain, Jason, breaking into space from midfield before feeding Shaquell Moore unopposed on the right-hand side, however, the right-back could not find a way past the spread-eagle shot-stopper, who did well to turn the attempt around the post with his left foot.
However, Levante's lack of prowess in front of goal almost proved costly once again, as Suarez found himself bearing down on goal with only the goalkeeper to beat.
Following the 30-year-old's scuffed initial effort, the striker had a second bite of the cherry, but a strong palm from Olazabal after a more precise attempt kept his side's deficit to two.
However, as the tie entered stoppage-time the Spanish goalkeeper could do nothing to stop Paulinho from getting his name on the scoresheet for the eight time this campaign, as the Brazilian tapped in from close range following Messi's squared ball across the face of goal.
The Catalonian's victory extends their unbeaten streak across all competitions to 26 and allowed Ernesto Valverde's side to regain their nine-point advantage over nearest rival Atletico Madrid in the race for the La Liga title.