Jose Barkero's deflected shot gave the hosts the perfect start after 13 minutes and things went from bad to worse for the visitors after half an hour.
Firstly goalkeeper Willy Caballero was sent off for handling outside the area and then, as the resulting free-kick rebounded off the wall, Juanlu fired the loose ball in for the second.
Arouna Kone scored the third before half-time following a shocking error from substitute keeper Ruben Martinez and Levante should have added to their tally in the second period but Ruben Suarez inexplicably shot over from 10 yards when perfectly placed.
Elsewhere, Helder Postiga scored twice to consign Real Sociedad to their third consecutive defeat and move Real Zaragoza into the top half of the table for the first time this season.
The Portuguese striker scored his first goal since joining from Sporting Lisbon with a stunning 11th minute overhead kick from the edge of the area that flew past Claudio Bravo in the Sociedad goal.
Both sides had chances as the game flowed from end to end in the first-half but Postiga scored the telling second goal just three minutes into the second period when he collected Leonardo Ponzio's fine through-ball and slotted past Bravo from close range.
Sevilla moved up to fourth after heaping more misery on winless Sporting Gijon and their under-pressure coach Manuel Preciado after a 2-1 victory.
The rock-bottom visitors battled hard and had their chances but poor finishing and some fine goalkeeping from Sevilla's Javi Varas kept them at bay.
A stunning opener from Manu del Moral set Sevilla on their way and the Andalucians moved two up courtesy of Martin Caceres' close-range header 12 minutes after half-time.
David Barral pulled one back but Sporting could not find an equaliser and remained three points adrift at the foot of the standings.
Ndri Romaric scored his first goal for Espanyol and the only goal of the game as the visitors recorded their first away win in 12 matches against Rayo Vallecano.
Espanyol had the better of the play throughout but were denied in the first-half by Rayo goalkeeper Dani Gimenez and had a couple of strong penalty claims waved away.
Romaric did eventually put his side in front with a calm finish after he was left all alone inside the area from Juan Forlin's pass.
The Ivorian also came closest to adding to the scoreline but his fine drive was turned away by Dani.
Lionel Messi reached another Barcelona landmark on Saturday with two more brilliant goals to inspire his side to a 3-0 victory over Racing Santander.
The Argentinian added the finish following a slick one-two with Andres Iniesta to move clear in second on the Catalan club's list of all-time top goalscorers.
And he rounded off the scoring with a simple finish after Iniesta had produced an outrageous piece of skill and shot against a post.
Messi's two goals were his 195th and 196th in all competitions for Barca and took him ahead of Laszlo Kubala on the all-time list.
Xavi scored with a rare header in between times as Barca remained one point ahead of Real Madrid at the top of the Primera Division and winless Racing remained in the bottom three.
Elsewhere on Saturday, Gonzalo Higuain's third hat-trick in his last four matches steered Real Madrid to an emphatic 4-1 home win over Real Betis.
The Argentinian hit a treble on his last Primera Division appearance for Madrid, away to Espanyol on October 2, and added another for his country in the World Cup qualifying match against Chile.
Higuain could not prevent Argentina stumbling to a 1-0 defeat against Venezuela on Tuesday, but he was back to full steam against Betis as Real Madrid ran riot after the break.
Kaka netted the other goal, while Jorge Molina scored for Betis.
Getafe and Villarreal did little to improve their disappointing starts to the season with a dire goalless draw on Saturday evening.
Real Mallorca enjoyed a dramatic start to life under new coach Joaquin Caparros after snatching a 1-1 draw against Valencia with a last-minute penalty.
Valencia looked certain to claim all three points after taking the lead through Adil Rami in the 38th minute. But the home side refused to throw in the towel and were rewarded for their persistence in the dying moments when Mehmet Topal was penalised for handball.
Striker Tomer Hemed accepted responsibility for the spot-kick and calmly slotted into the bottom corner.
Atletico Madrid were left still searching for their first away win of the season after being held to a goalless draw by promoted Granada.
Ikechukwu Uche looked to have given the home side the lead, but his header from near the penalty spot came back off the post with Atletico goalkeeper Thibaut Courtois well beaten.
Granada defender Inigo Lopez then headed a free-kick just wide before Dani Benitez missed a gilt-edged chance in the 20th minute when an Atletico defensive error left him one-on-one with Courtois, but his chip over the Atletico goalkeeper dropped just beyond the far post.
Soon after that Atletico had a great chance themselves, but Jose Antonio Reyes was denied by a superb one-handed save by Roberto Fernandez following a slick move by the visitors.
Guilherme Siqueira also saw his goal-bound shot blocked by a crucial last-ditch intervention by Filipe Luis.