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.
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.
