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.
However, Valencia were on terms for just one minute, with Jose Luis Morales cutting inside from the right wing to curl in a superb left-footed winner from the edge of the penalty area.
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.
Mario Gaspar and Gerard Moreno gave Villarreal a 2-0 half-time advantage on their way to posting a 2-1 victory over Getafe.
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.
Elche came from two goals down to rescue a 2-2 draw and deny Cordoba an important victory in the battle against relegation.
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.
Elche hit back through a David Lomban penalty, before Jonathas atoned for his earlier error by converting a superb left-footed volley to ensure a share of the spoils.