Messi's goals were both laid on by Andres Iniesta who also hit the target himself before supplying Cesc Fabregas for the fourth.
The Argentine's brace means he now has 82 goals in 2012, just three short of German legend Gerd Mueller's all-time calendar record of 85 set in 1972.
He also tops the La Liga charts for the season with 19 goals.
Atletico had earlier beaten Sevilla 4-0 to keep pace at the top and go eight points ahead of city rivals Real Madrid in third who had lost 1-0 at Betis on Saturday.
Barca's win increased their gap over Real Madrid to 11 points.
They have also equalled Real's record for the best start to a La Liga season set in 1991-92.
But coach Tito Vilanova does not see the league as being won so early in the season.
"The league is not over, we're only a third through and Atletico are three points behind us. There is a lot to play for. We have been 11 ahead of Madrid before and we suffered a lot in the end," he said.
Barca had struggled in the first half and their cause was not helped by losing Dani Alves after only 13 minutes with what appeared to be a recurrence of a recent hamstring injury.
When his replacement Martin Montoya took the pitch it meant Barca's full side had also starred for the club at youth level.
Afterwards Xavi Hernandez praised a blueprint set out by former coach Louis Van Gaal.
"It's an amazing and extraordinary feat, we're proud of the work of our youth system, I've lived through this since it was just Puyol and me in the first team. Van Gaal always said it, we have to play to with an eleven from the club. I take the opportunity to send my regards to Van Gaal," he said.
Jose Maria Barkero had the best chance of the opening exchanges for Levante, drawing Barca goalkeeper Victor Valdes into a save with a 12th-minute drive.
Barca took 10 minutes to react, Messi hitting a low shot that missed just wide right, a minute before Xavi Hernandez hit a similar drive that went to the left.
The Catalans' intricate build-up play was comfortably contained by solid defending from the home team in a tight first period.
Levante, in the meantime, looked dangerous on the counter-attack and Obafemi Martins narrowly glanced a header wide just before half-time.
However, Barca finally found a way through just after the break and it was from a perfectly threaded pass from Iniesta that allowed Messi to coolly slot home.
Five minutes later, Iniesta was the provider again, the little midfielder pulling back the ball for Messi to double the lead.
Another five minutes had passed before Iniesta buried Levante's challenge for good with a drive from the edge of the area.
The fourth came on 63 minutes, this time Fabregas was given the simple task of finishing off another Iniesta pass.
Barca had solved what had at first seemed a difficult task with four goals in 18 second-half minutes and for Levante there was no way back.
Valdes made matters worse for the home side making a double save from a Barkero penalty in the dying minutes after Carles Puyol had handled in the area.
For Atletico, Radamel Falcao, Arda Turan and Koke got first-half goals and Miranda one in the last minute to make it seven straight home wins in the league against a Sevilla side that played with only 10 men from the 22th minute and finished with nine.
Atletico made a breakthrough on 19 minutes when Koke was pulled down by Federico Fazio, who received a straight red.
Falcao smashed the penalty straight down the middle of the goal for his 11th league goal of the season and Sevilla were facing more than an hour of play with ten men.
On 38 minutes, Turan doubled the home side's lead when Falcao received a defensive clearance and broke at speed before releasing the Turkish winger, who hit a shot that caught a slight deflection of Spahic on the way to goal.
On the stroke of half-time, Koke stroked home a Diego Costa cross for the third.
It was one way traffic in the second period but Sevilla held firm for most of it, despite losing Ivan Rakitic to a second yellow card on 83 minutes, before Miranda hit the fourth from close range in injury time.
Also on Sunday, Athletic Bilbao and Deportivo La Coruna shared the points in a 1-1 draw in the San Mames stadium.
Oscar de Marcos put the home side ahead on 24 minutes when he converted a Markel Susaeta cross, but against the run of play Abel Aguilar hit an equaliser early in the second-half to earn Deportivo a point and move his side out of the relegation zone.
Getafe won 2-0 at Espanyol to keep the Barcelona side bottom of the table, two points behind Deportivo.
Pedro Leon put Getafe ahead on 15 minutes before Mane doubled the lead in the last minute.