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.
Champions Barcelona, bidding for a club record-equalling fourth straight title, were a point back in second after a Lionel Messi-inspired 5-0 demolition of Real Mallorca on Saturday, with Levante third on 23 points.
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.
Atletico Madrid secured their first win in six games when Spain Under-21 striker Adrian scored twice in a 3-1 success at home to Real Zaragoza, easing pressure on new coach Gregorio Manzano.
Bilbao and Atletico both have 13 points, with the Basques ahead on goal difference in ninth and the Madrid side in 10th.
Real Betis won their opening four games of the campaign after gaining promotion to the top flight at the end of last season but have now lost six in a row after they were beaten 1-0 at Racing Santander and slipped to 12th on 12 points.
Sevilla can close to within a point of fourth-placed Valencia, who beat Getafe 3-1 on Saturday, when they play at home to promoted Andalusian rivals Granada in the Monday match.
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