The Mestalla outfit came into the weekend third in the Spanish top flight, but were unable to get the better of their near neighbours as they slipped to fourth.
Victor Casadesus' 58th-minute header prompted jubilant scenes among the home fans at Estadio Ciudad de Valencia, but that joy was tempered when Dani Parejo slotted home to pull the visitors level 17 minutes from time.
The victory - Levante's third of the season - lifts Lucas Alcaraz's men out of the bottom three, while Valencia are now six points adrift of leaders Real Madrid.
Rayo Vallecano also picked up a valuable three points - emerging as 1-0 victors from their clash with Celta Vigo.
Alberto Bueno scored the only goal of the encounter by getting his head to a whipped Gael Kakuta cross to divert the ball beyond goalkeeper Sergio Alvarez.
Mehdi Lacen's 20-yard strike shortly after the hour mark proved to be a mere consolation for the visitors, who saw their hosts bring an end to a three-match winless run.
The two sides remain in the bottom three, but it could have been different for Cordoba, who saw Fidel and Federico Cartabia give them a comfortable lead after Jonathas had missed a sixth-minute penalty at Estadio Manuel Martinez Valero.
