The Valencia-based club, whose annual budget of around 20 million euros is less than a 20th of new leaders Real Madrid, fell behind to an Alvaro Cejudo strike in the 39th minute and Nino netted a second for Pamplona-based Osasuna three minutes later.
Cejudo, who had already been booked for taking his shirt off in his goal celebration, was shown a second yellow card in the 59th minute but Levante were unable to exploit their numerical advantage and their astounding seven-match winning streak came to an end.
"It's true that we have been on a very good run but we knew this was going to be a tough match," Levante coach Juan Ignacio Martinez, who is in his debut top-flight campaign, said at a news conference.
"When you have won so many games the next defeat is always closer," he added.
La Liga had a more familiar look to it after Levante were toppled from the summit, with Real Madrid leading on 25 points from 10 matches thanks to Saturday's 1-0 win at Real Sociedad.
In Sunday's late kick-off, big-spending Malaga climbed above Espanyol into sixth when they beat the Catalan capital's second club 2-1 at the Rosaleda.
Athletic Bilbao were held to a 1-1 draw at Sporting Gijon, Croatian substitute Mate Bilic grabbing an equaliser for the hosts after Markel Susaeta's 63rd-minute effort.
