Victor Casadesus nodded Levante in front in the 58th minute at the Ciutat de Valencia stadium before Dani Parejo levelled in the 73rd when he was sent clear by Alvaro Negredo.
Substitute Jose Luis Morales struck the winner moments later when he ran at the visiting defence and curled a superb shot into the top corner.
Negredo, on loan from Manchester City, had a chance to equalise again eight minutes from time but sent his header straight at keeper Diego Marino.
“We have to congratulate our opponent because they achieved the victory but it is hard to understand when you don’t win despite being very superior,” Valencia coach Nuno told a news conference.
“Now we have to pick ourselves up very quickly from defeat in a match into which we put everything we had,” added the Portuguese who took over from Argentina-born Juan Antonio Pizzi in July.
“Levante limited themselves to defending and they do it very well but we deserved the win and I am very proud of the team. This result could help us improve.”
Hopes are high at Valencia that a takeover of the club by Singapore billionaire Peter Lim will end years of financial struggle and restore their status as genuine challengers for silverware in Spain and Europe.
They last won La Liga under Rafa Benitez in 2004 and were losing Champions League finalists in 2000 and 2001.
With 12 matches played Valencia are fourth on 24 points, two behind third-placed champions Atletico Madrid who won 3-1 at home to Malaga on Saturday.
Real Madrid lead on 30 points after Saturday’s 4-0 stroll at La Liga debutants Eibar, with a Cristiano Ronaldo double taking the Portugal forward’s tally for the season to 20 goals in 11 appearances.
Barcelona are two points behind their arch rivals in second thanks to Saturday’s 5-1 drubbing of fifth-placed Sevilla that was decorated by Lionel Messi netting a hat-trick to set an all-time La Liga record of 253 goals.
The 27-year-old Argentina maestro surpassed the previous best of 251 set by former Athletic Bilbao striker Telmo Zarra in 1955.
Levante’s victory lifted them out of the relegation zone to 13th place on 12 points, two behind Rayo Vallecano who won 1-0 at home to Celta Vigo in Sunday’s early kickoff.
“Derby days are always special days and we had to work hard to get the three points,” Morales said.
“Protecting our top-flight status will happen in home matches and above all with the support of our fans. It could be the best goal I have scored in my career.”
Villarreal closed to within two points of seventh-placed Celta after they won 2-1 at Getafe, while bottom side Cordoba were denied a first win of the campaign when they let slip a two-goal lead and drew 2-2 at fellow strugglers Elche.
(Editing by Ian Chadband/Greg Stutchbury)