The tiny Valencia-based club, who have an annual budget of only 20 million euros compared with Real's of almost 500 million, have 20 points from eight matches, including three from a shock 1-0 home win over the big-spending Madrid side last month.
Midfielder Juanlu, one of a slew of Levante players over 30, netted twice in the first half at the Madrigal and Arouna Kone struck 13 minutes into the second period as Juan Ignacio Martinez's unfancied side secured a sixth straight win.
Villarreal, competing in this season's Champions League after finishing fourth last term, are languishing in 16th on just seven points.
Jose Mourinho's Real were the overnight leaders on 19 after they thrashed Malaga 4-0 on Saturday thanks to a hat-trick from the world's most expensive player Cristiano Ronaldo.
Champions Barcelona, bidding for a fourth consecutive title, slipped to third on 18 after they were held to a 0-0 draw at home to Sevilla, in fourth on 16.
The match at the Nou Camp ended in acrimony after Barca were awarded a stoppage-time penalty and a mass brawl erupted which led to the dismissal of Sevilla striker Frederic Kanoute.
Goalkeeper Javi Varas saved Lionel Messi's spot-kick before the visitors had defender Fernando Navarro sent off for a wild tackle on Pedro.
In Sunday's earlier kick-offs, Roberto Soldado slotted an 89th-minute equaliser for Valencia in a 1-1 draw at home to Athletic Bilbao after Iker Muniain had put the visitors ahead with around 20 minutes left with a splendid run and shot.
Former Real Madrid and Getafe striker Soldado, who is pushing for a place in the Spain squad, took his tally to six for the season, four behind joint top scorers Messi and Ronaldo.
Atletico Madrid were held to a 1-1 draw at home to Real Mallorca, their fourth stalemate of the campaign, with both goals coming from the penalty spot.
Early pace-setters Real Betis won their opening four games after gaining promotion to the top flight at the end of last season but have now lost four in a row after they were beaten 2-0 at home to Rayo Vallecano.
Osasuna thumped visiting Real Zaragoza 3-0 and Real Sociedad drew 0-0 at home to Getafe.
