Atletico Madrid claimed 1-1 draw to prevent city rivals Real from grabbing first place on a weekend where none of the top six were victorious in La Liga.
Following Barcelona's 2-1 defeat at Sevilla on Saturday, surprise early pacesetters Villarreal had a chance to extend their advantage at Levante.
But Bojan Jokic earned a 36th-minute red card for his second booking to hinder Marcelino's side and Brazilian forward Deyverson scored the only goal seven minutes from time to lift Levante off the foot of the table.
It meant a win at the Vicente Calderon would lift Real to the summit – a result they were well-placed to achieve when Karim Benzema headed them into an early lead and the France striker's countryman Antoine Griezmann missed a first-half penalty for Atletico.
However, Real are now winless at the home of their near neighbours in their past six attempts after substitute Luciano Vietto poached his first goal from the club in the 83rd minute.
Athletic Bilbao ended a run of four matches without a win by beating Valencia 3-1.
Dani Parejo put Nuno Espirito Santo's men ahead after 20 minutes with a magnificent free-kick but Aymeric Laporte's header ensured Athletic went in at the break all square.
The San Mames crowd were then thrilled by a stirring second-half display, which brought goals from Markel Susaeta and former Valencia striker Aritz Aduriz.
In Sunday's other game, Ruben Castro inspired Real Betis to their first win at Rayo Vallecano since 1999.
Heiko Westermann played a one-two with Castro to break the deadlock and the veteran forward sealed a 2-0 triumph after the hour.
